Prasanna

You can Download Samacheer Kalvi 10th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.16

10th Maths Exercise 3.16 Solution Question 1.
In the matrix A = \(\left[\begin{array}{cccc}{8} & {9} & {4} & {3} \\ {-1} & {\sqrt{7}} & {\frac{\sqrt{3}}{2}} & {5} \\ {1} & {4} & {3} & {0} \\ {6} & {8} & {-11} & {1}\end{array}\right]\)
(i) The number of elements
(ii) The order of the matrix
(iii) Write the elements a₂₂, a₂₃, a₂₄, a₃₄, a₄₃, a₄₄
Solution:
(i) 16
(ii) 4 × 4
(iii) \(\sqrt{7}, \frac{\sqrt{3}}{2}\), 5, 0, -11, 1

10th Maths Exercise 3.16 Solutions Question 2.
If a matrix has 18 elements, what are the possible orders it can have? What if it has 6 elements?
Solution:
1 × 18, 2 × 9, 3 × 6, 6 × 3, 9 × 2, 18 × 1 and 1 × 6, 2 × 3, 3 × 2, 6 × 1

10th Maths Exercise 3.16 Answers Question 3.
Construct a 3 × 3 matrix whose elements are given by then find the transpose of A.
(i) a_ij = |i – 2j|
(ii) a_ij = \(\frac{(i+j)^{3}}{3}\)
Solution:
(i) a_ij = |i – 2j|
a₁₁ = |1 – 2 × 1| = |1 – 2| = |-1| = 1
a₁₂ = |1 – 2 × 2| = |1 – 4| = |-3| = 3
a₁₃ = |1 – 2 × 3| = |1 – 6| = |-5| = 5
a₂₁ = |2 – 2 × 1| = |2 – 2| = 0
a₂₂ = |2 – 2 × 2| = |2 – 4| = |-2| = 2
a₂₃ = |2 – 2 × 3| = |2 – 6| = |-4| = 4
a₃₁ = |3 – 2 × 1| = |3 – 2| = |1| = 1
a₃₂ = |3 – 2 × 2| = |3 – 4| = |-1| = 1
a₃₃ = |3 – 2 × 3| = |3 – 6| = |-3| = 3
∴ \(\left[\begin{array}{lll}{1} & {3} & {5} \\ {0} & {2} & {4} \\ {1} & {1} & {3}\end{array}\right]\) is the required 3 × 3 matrix

Ex 3.16 Class 10 Samacheer Question 4.

Solution:

10th Maths Exercise 3.16 Question 5.

Solution:

10th Maths 3.16 Question 6.

Solution:

Exercise 3.16 Class 10 Question 7.
Find the values of x,y and z from the following equations

Solution:

You can Download Samacheer Kalvi 11th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.1

11th Maths Exercise 7.1 Answers Question 1.
Construct an m × n matrix A = [a_ij], where a_ij is given by

Solution:
(i) a_ij = \(\frac{(i-2 j)^{2}}{2}\)
Here m = 2, n = 3
So we have to construct a matrix of order 2 × 3

(ii) Here m = 3 and n = 4
So we have to construct a matrix order 3 × 4
The general form of a matrix of order 3 × 4 will be

11th Maths Exercise 7.1 Question 2.
Find the values of p, q, r and s if

Solution:
When two matrices (of same order) are equal then their corresponding entries are equal.

⇒ p² – 1 = 1
⇒ p² = 1 + 1 = 2
p = ± \(\sqrt{2}\)
-31 – q³ = -4
-q³ = -4 + 31 = 27
q³ = -27 = (-3)³
⇒ q = -3
r + 1 = \(\frac{3}{2}\)
⇒ r = \(\frac{3}{2}\) – 1 = \(\frac{3-2}{2}\) = \(\frac{1}{2}\)
s – 1 = π
⇒ s = – π + 1 (i.e.,) s = 1 – π
So, p = ± \(\sqrt{2}\), q = -3, r = 1/2 and s = 1 – π

11th Maths Matrices And Determinants Solutions Question 3.
Determine the value of x + y if
Solution:
\(\left[\begin{array}{cc}{2 x+y} & {4 x} \\ {5 x-7} & {4 x}\end{array}\right]=\left[\begin{array}{cc}{7} & {7 y-13} \\ {y} & {x+6}\end{array}\right]\)
⇒ 2x + y = 7 ………….. (1)
4x = 7y – 13 ………….. (2)
5x – 7 = y …………… (3)
4x = x + 6 ……………. (4)
from (4) 4x – x = 6
3x = 6 ⇒ x = \(\frac{6}{3}\) = 2
Substituting x = 2 in (1), we get
2(2) + y = 7 ⇒ 4 + y = 7 ⇒ y = 7 – 4 = 3
So x = 2 and y = 3
∴ x + y = 2 + 3 = 5

11th Maths 7.1 Exercise Question 4.
Determine the matrices A and B if they satisfy

Solution:

11th Maths Volume 2 Exercise 7.1 Question 5.
If A = \(\left[\begin{array}{ll}{\mathbf{1}} & {\boldsymbol{a}} \\ {\mathbf{0}} & {\mathbf{1}}\end{array}\right]\), then compute A⁴
Solution:

11th Maths Matrix Solutions Question 6.
Consider the matrix A_α = \(\left[\begin{array}{cc}{\cos \alpha} & {-\sin \alpha} \\ {\sin \alpha} & {\cos \alpha}\end{array}\right]\)
(i) Show that A_αA_β = A_{α + β}.
(ii) Find all possible real values of satisfying the condition A_α + A^T_α = 1.
Solution:

General solution is α = 2nπ + \(\frac{\pi}{3}\), n ∈ Z

11th Maths Exercise 7.1 Tamil Medium Question 7.
If A = \(\left[\begin{array}{rr}{4} & {2} \\ {-1} & {x}\end{array}\right]\) such that (A – 2I) (A – 3I) = 0, find the value of x.
Solution:

11th Maths Matrices And Determinants Pdf Question 8.
If A = \(\left[\begin{array}{ccc}{\mathbf{1}} & {\mathbf{0}} & {\mathbf{0}} \\ {\mathbf{0}} & {\mathbf{1}} & {\mathbf{0}} \\ {\boldsymbol{a}} & {\boldsymbol{b}} & {-\mathbf{1}}\end{array}\right]\), show that A² is a unit matrix.
Solution:

Exercise 7.1 Class 11 Maths State Board Question 9.
If A = and A³ – 6A² + 7A + KI = 0, find the value of k.
Solution:

11th Maths 7.1 Question 10.
Give your own examples of matrices satisfying the following conditions in each case:
(i) A and B such that AB ≠ BA.
(ii) A and B such that AB = 0 = BA, A ≠ 0 and B ≠ 0.
(iii) A and B such that AB = 0 and BA ≠ 0.
Solution:

11th Maths Matrix And Determinants Question 11.
Show that f(x) f(y) = f(x + y), where f(x) =
Solution:

11th Maths Exercise 7.1 In Tamil Question 12.
If A is a square matrix such that A² = A, find the value of 7A – (I + A)³.
Solution:
Given A² = A
So 7A – (I + A)³ = 7A – (I + 3A + 3A² + A³]
= 7A – I – 3A – 3 A² – A³
Given A² = A
7A – I – 3A – 3A – A³ = -I + A – A³
= -I + A – (A² × A)
= -I + A – (A × A) = -I + A – A²
= -I + A – A = -I
So the value of 7A – (I + A)³ = -I.

Question 13.
Verify the property A (B + C) = AB + AC, when the matrices A, B and C are given by

Solution:

11th Maths Volume 2 Exercise 7.1 Answers Question 14.
Find the matrix A which satisfies the matrix relation
Solution:

11 Maths Exercise 7.1 Question 15.

(i) (A + B)^T = A^T + B^T = B^T + A^T
(ii) (A – B)^T = A^T – B^T
(iii) (B^T)^T = B.
Solution:

11th Maths 7th Chapter Question 16.
If A is a 3 × 4 matrix and B is a matrix such that both ATB and BAT are defined, what is the order of the matrix B?
Sol.
A is a matrix of order 3 × 4
So AT will be a matrix of order 4 × 3
AT B will be defined when B is a matrix of order 3 × n
BA^T will be defirted when B is of order m × 4
from (1) and (2) we see that B should be a matrix of order 3 × 4

Question 17.
Express the following matrices as the sum of a symmetric matrix and a skew-symmetric matrix:

Solution:

Matrices And Determinants Class 11 State Board Solutions Question 18.
Find the matrix A such that
Solution:

11th Maths Determinants Solutions Question 19.
If A = is a matrix such that AA^T = 9I, find the values of x and y.
Solution:

Question 20.

Solution:

Class 11th Maths Exercise 7.1 Question 21.
Construct the matrix A = [a_ij]_3×3, where a_ij = i- j. State whether A is symmetric or skew- symmetric.
Solution:
Given A is a matrix of order 3 × 3

Here A^T = -A
⇒ A is skew symmetric

Matrices And Determinants Class 11 Solutions Pdf Question 22.
Let A and B be two symmetric matrices. Prove that AB = BA if and only if AB is a symmetric matrix.
Solution:
Let A and B be two symmetric matrices
⇒ A^T = A and B^T = B …………….. (1)
Given that AB = BA (2)
To prove AB is symmetric:
Now (AB)^T = B^TA^T = BA
(from(1)) But (AB)^T = AB by ………….. (2)
⇒ AB is symmetric.
Conversely let AB be a symmetric matrix.
⇒ (AB)^T = AB
i.e. B^TA^T = AB
i.e. BA = AB (from (1))
⇒ AB is symmetric

Samacheer Kalvi 11th Maths Solutions Question 23.
If A and B are symmetric matrices of same order, prove that
(i) AB + BA is a symmetric matrix.
(li) AB – BA is a skew-symmetric matrix.
Solution:
Given A and B are symmetric matrices
⇒ – A^T = A and B^T = B
(i) To prove AB + BA is a symmetric matrix.
Proof: Now (AB + BA)^T = (AB)^T + (BA)^T = B^TA^T + A^TB^T
= BA + AB = AB + BA
i.e. (AB + BA)^T = AB + BA
⇒ (AB + BA) is a symmetric matrix.
(ii) To prove AB – BA is a skew symmetric matrix.
Proof: (AB – BA)^T = (AB)^T – (BA)^T = B^TA^T – A^TB^T = BA – AB
i.e. (AB – BA)^T = – (AB – BA)
⇒ AB – BA is a skew symmetric matrix.

11th Maths 7th Lesson Question 24.
A shopkeeper in a Nuts and Spices shop makes gift packs of cashew nuts, raisins and almonds.
Pack I contains 100 gm of cashew nuts, 100 gm of raisins and 50 gm of almonds. Pack-II contains 200 gm of cashew nuts, 100 gm of raisins and 100 gm of almonds. Pack-III contains 250 gm of cashew nuts, 250 gm of raisins and 150 gm of almonds. The cost of 50 gm of cashew nuts is ₹ 50, 50 gm of raisins is ₹ 10, and 50 gm of almonds is₹ 60. What is the cost of each gift pack?
Solution:

Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.1 Additional Problems

Class 11 Maths Ex 7.1 Solutions Question 1.

Prove that (i) AB ≠ BA
(ii) A(BC) = (AB) C
(iii) A(B + C) = AB + AC
(iv) AI = IA = A
Solution:

Class 11th Maths Chapter 7 Exercise 7.1 Question 2.
If A = \(\left[\begin{array}{ll}{2} & {3} \\ {4} & {5}\end{array}\right]\) find A² – 7A – 2I.
Solution:

11th Maths Guide Question 3.

Solution:

11th Maths Guide Question 4.

Solution:

Question 5.
If A = \(\left[\begin{array}{rr}{3} & {-5} \\ {-4} & {2}\end{array}\right]\), show that A² – 5A – 14I = 0 where I is the unit matrix of order 2.
Solution:

Question 6.
If A = \(\left[\begin{array}{rr}{3} & {-2} \\ {4} & {-2}\end{array}\right]\), find k so that A² = kA – 2I
Solution:

Question 7.
If A = \(\left[\begin{array}{lll}{1} & {2} & {2} \\ {2} & {1} & {2} \\ {2} & {2} & {1}\end{array}\right]\), show that A² – 4A – 5I = 0
Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

You can Download Samacheer Kalvi 9th Social Science Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Samacheer Kalvi 9th Social Science Civics Solutions Chapter 1 Forms of Government and Democracy

Forms of Government and Democracy Textual Exercise

I. Choose the correct answer.

Forms Of Government And Democracy Class 9 Question 1.
A system of government in which one person reigns supreme, usually a king or queen, is called ……..
(a) autocracy
(b) monarchy
(c) democracy
(d) republic
Answer:
(b) monarchy

Mention The Forms Of Democracy Class 9 Question 2.
A system of government by one person with absolute power.
(a) Aristocracy
(b) Theocracy
(c) Democracy
(d) Autocracy
Answer:
(d) Autocracy

Forms Of Government And Democracy Book Back Answers Question 3.
When a country is governed by a few privileged, the form of government is called ……
(a) Aristocracy
(b) Parliamentary
(c) Democracy
(d) Republic
Answer:
(a) Aristocracy

9th Social Civics Guide Question 4.
Former Soviet Union is an example for ……
(a) aristocracy
(b) theocracy
(c) oligarchy
(d) republic
Answer:
(c) oligarchy

Forms Of Government Class 9 Question 5.
Select the odd one ……
(a) India
(b) USA
(c) France
(d) Vatican
Answer:
(d) Vatican

9th Social Guide Civics Question 6.
Abraham Lincoln was the President of the
(a) USA
(b) UK
(c) USSR
(d) India
Answer:
(a) USA

Forms Of Government And Democracy Question 7.
Kudavolai system was followed by ……….
(a) Gheras
(b) Pandyas
(c) Cholas
(d) Kalabhras
Answer:
(c) Cholas

Give Abraham Lincoln’s Definition For Democracy Question 8.
Direct Democracy in olden times existed ………
(a) In the republics of ancient India
(b) Among the USA
(c) In the city-state of ancient Athens
(d) Among the UK
Answer:
(c) In the city-state of ancient Athens

9th Social Solutions Samacheer Kalvi Question 9.
In which country has democracy originated? .
(a) India
(b) Switzerland
(c) USA
(d) Athens
Answer:
(d) Athens

Samacheer Kalvi 9th Social Science Civics Book Solutions Question 10.
From which language was the term “Democracy” derived?
(a) Greek
(b) Latin
(c) Persian
(d) Arabic
Answer:
(a) Greek

Samacheer Kalvi Guru 9th Social Science Question 11.
In democracy the final authority rests with ………
(a) The Parliament
(b) The People
(c) The council of Ministers
(d) The President
Answer:
(b) The People

Question 12.
Which one of the country has Presidential form of government?
(a) India
(b) Britain
(c) Canada
(d) USA
Answer:
(d) USA

Question 13.
The largest democratic country in the world is ……..
(a) Canada
(b) India
(c) USA
(d) China
Answer:
(b) India

Question 14.
Assertion (A): Direct democracy is practised in Switzerland.
Reason (R): People directly participates in decision making.
(a) Both (A) and (R) are true and (R) explains (A)
(b) Both (A) and (R) are true and (R) does not explain (A)
(c) (A) is correct and (R) is false
(d) (A) is false and (R) is true
Answer:
(a) Both (A) and (R) are true and (R) explains (A)

Question 15.
Assertion (A): India has parliamentary form of democracy.
Reason (R): Indian parliament comprises two houses.
(a) Both (A) and (R) are true and (R) explains (A)
(b) Both (A) and (R) are true and (R) does not explain (A)
(c) (A) is correct and (R) is false
(d) (A) is false and (R) is true
Answer:
(a) Both (A) and (R) are true and (R) explains (A)

Question 16.
The meaning of Franchise is ………
(a) Right to elect
(b) Right to vote for the poor
(c) Right to vote
(d) Right to vote for the rich
Answer:
(c) Right to vote

Question 17.
The grant of universal franchise creates ………….
(a) Social equality
(b) Economic equality
(c) Political equality
(d) Legal equality
Answer:
(c) Political equality

Question 18.
Prime Minister of India is appointed by …….
(a) Lok Sabha
(b) Rajya Sabha
(c) Speaker
(d) President
Answer:
(d) President

Question 19.
The President of India can nominate ……….
(a) 12 members to Lok Sabha
(b) 2 members of Rajya Sabha
(c) 12 members to Rajya Sabha
(d) 14 members of Rajya Sabha
Answer:
(c) 12 members to Rajya Sabha

Question 20.
The First general elections after independence in India were held in …………
(a) 1948
(b) 1952
(c) 1957
(d) 1947
Answer:
(b) 1952

II. Fill in the blanks.

1. The Constitution of India was finally adopted on ………
2. The two types of democracy are …….. and ……….
3. An example for direct democracy is ………
4. India has a …….. form of democracy.
5. …….. was the first Prime Minister of independent India.
6. The first general elections were held in British India in the year …….
7. The Parliament House in India was designed by …… and ……….
Answers:
1. 26th November 1949
2. Direct and Indirect
3. Switzerland
4. Parliamentary
5. Jawaharlal Nehru
6. 1920
7. Edwin Lutyens and Herbert Baker

III. Match the following.

Answers:
1. (d)
2. (a)
3. (b)
4. (c)

IV. Give short answers.

Question 1.
Give Abraham Lincoln’s definition for democracy.
Answer:
Abraham Lincoln defines democracy as a government of the people, by the people and for the people.

Question 2.
Mention the forms of democracy.
Answer:

Question 3.
Distinguish between direct and indirect democracy.
Answer:

V. Answer in detail.

Question 1.
What are the challenges to democracy? Explain.
Answer:
Democracy is the dominant form of government in the contemporary world. It has not faced a serious challenge or a rival so far. In the last hundred years, there has been an expansion of democracy all over the world. The various aspects of democracy and its challenges are:

1. Illiteracy
2. Poverty
3. Gender discrimination
4. Regionalism
5. Casteism, communalism and religious fundamentalism
6. Corruption
7. Criminalisation of politics.
8. Political violence

Question 2.
Explain the conditions necessary for the success of democracy in India.
Answer:

1. Empowerment of the poor and illiterates to enjoy the goodness of democracy.
2. Willingness among the elected people not to misuse their powerful position and public wealth.
3. Eradication of social evils and dangers from which democracy suffers.
4. An impartial and efficient press to form public opinion.
5. Presence of strong public opinion.
6. Feeling of tolerance and communal harmony among the people.
7. Awareness among the people of the fundamental rights that they are entitled to enjoy.
8. Conscious check and vigilance on the working of the elected representatives.
9. Powerful and responsible opposition.

Question 3.
What is your opinion about democracy in India?
Answer:
India has a parliamentary form of democracy. The Indian Parliament comprises the elected representatives of people and makes the laws for the Country. The participation of people in the decision making and the consent of citizens are the two important elements of the parliamentary form of government in India.

India is the largest democratic country in the world. Democracy in India works on five basic principles. These are sovereign, socialist, secular, democratic, republic.

Every person who is a citizen of India and who is not less than 18 years of age can exercise their right to vote in India, based on universal adult suffrage. There is no discrimination based on a person’s caste, creed, religion, region, gender and education when it comes to providing the right to vote.

VI. Project and Activity.

Question 1.
Discuss in the class what is universal adult franchise? Why is it important?
Answer:

1. The teacher arranges a discussion session.
2. The students will be divided into two groups to discuss on the above content.

Universal Adult Franchise: The Article 326 of the Indian Constitution grants universal adult suffrage, according to which every adult citizen is entitled to cast his/her vote in all state elections unless that citizen is convicted of certain criminal offences (or) deemed unsound of mind.

Why is it important?

1. It has nothing to do with economic growth, or staying ahead, of the competition. Under this system a government is elected that is accountable to the people it governs.
2. Because every vote counts, issues in a society receive their appropriate weight in terms of importance and urgency. ,

Question 2.
“Democracy is the power of majority which respects minority.” Discuss.
Answer:

1. Democracy requires, minority rights equally as it does majority rule.
2. Indeed, as democracy is understood today the minority’s rights must be protected no matter how alienated a minority is from the majority society. Otherwise the minority rights lose their meaning.

Question 3.
Conduct a mock election in your class.
Answer:
Election activities in the class room

1. Campaigning
2. Voting Booth
3. Voter Registration form
4. Campaign posters
5. Cast your Ballot
6. Reward your voters
7. Tally up the votes
8. Graph the votes.

• Before beginning, think of issues, students enjoy voting on, make up copies of a short voter registration form for each student.
• Have a ballot box.
• After the election issue is chosen you will need to make up a ballot for each student.

Question 4.
A group discussion on the merits and demerits of democracy of India in the classroom.
Answer:
Merits and Demerits of Democracy:
Merits

1. Responsible and accountable government.
2. Equality and fraternity.
3. Sense of responsibility among common people.
4. Local self-government.
5. Development and prosperity for all.
6. Popular sovereignty.
7. Sense of cooperation and fraternal feeling

Demerits

1. Indirect or representative nature of democracy.
2. Lack of interest in democratic process and hence lower turnout in elections.
3. Instability in governance due to fractured mandate.
4. Delay in decision – making process.

VII. HOTS

Question 1.
Will you have the right to equality under dictatorship? What would be the attitude regarding public opinion in such a country?
Answer:
No; well, a dictatorship is when a country is run by a minority of people and the citizens of that country don’t have a choice of who runs it. If one person has to make all the decisions for a country, they might use their power badly because they have too much responsibility.

Question 2.
How does democracy lead to a peaceful and a harmonious life among the citizens? Explain.
Answer:
Democracy safeguards the fundamental rights which are defined as basic human freedoms which every Indian citizen has the right to enjoy for a proper and harmonious development of personality.

The students can refer and download from the Internet.

VIII. Life Skills

Select a group of countries, Research each country and tell what type of government it has: Aristoracy, Monarchy, Autocracy, Oligarchy, Theocracy, Democracy, Republic. Then, provide characteristics of this country that helped you determine the type of government.

The teacher can assign this as a Project & Group Activity for the students.

Forms of Government and Democracy Additional Questions

I. Choose the correct answer.

Question 1.
A system of government by one person with absolute power is ……
(a) Autocracy
(b) Aristocracy
(c) Monarchy
(d) Oligarchy
Answer:
(a) Autocracy

Question 2.
Democracy as a government of the people, by the people and for the people defined by ……..
(a) Mahatma Gandhi
(b) Jawaharlal Nehru
(c) Abraham Lincoln
(d) Herbert Baker
Answer:
(c) Abraham Lincoln

Question 3.
Democracy began ………. years ago.
(a) 2000
(b) 2500
(c) 3000
(d) 3200
Answer:
(b) 2500

Question 4.
Kudavolai system was a very notable and unique feature of the village administration of …….
(a) Cheras
(b) Cholas
(c) Pandyas
(d) Pallavas
Answer:
(b) Cholas

Question 5.
This is the dominant form of government in the contemporary world.
(a) Oligarchy
(b) Monarchy
(c) Theocracy
(d) Democracy
Answer:
(d) Democracy

Question 6.
Assertion (A): The term ‘democracy’ is derived from two Greek words demos meaning people and cratia meaning power.
Reason (R): Literally democracy means “the power of the people”.
(a) Both (A) and (R) are true and (R) explains (A)
(b) Both (A) and (R) are true (A) explains (R)
(c) (A) is correct and (R) is false
(d) (A) is false and (R) is true
Answer:
(a) Both (A) and (R) are true and (R) explains (A)

Question 7.
Assertion (A): India has a parliamentary form of democracy.
Reason (R): The Indian Parliament comprises the elected representatives of people.
(a) Both (A) and (R) are true and (R) explains (A)
(b) Both (A) and (R) are true (A) explains (R)
(c) (A) is correct and (R) is false
(d) (A) is false and (R) is true
Answer:
(a) Both (A) and (R) are true and (R) explains (A)

Question 8.
Indian citizen above years of age can exercise the right to vote in India.
(a) 16
(b) 17
(c) 18
(d) 19
Answer:
(c) 18

II. Fill in the blanks.

1. The modern world prefers ……….
2. The democratic institutions existed in India as early as the …….. period.
3. An example for Indirect Democracy is ……….
4. India has a …….. government with elected representatives at the federal, state and local
levels.
5. The two houses of our Parliament are ………. and ………
6. A group of people living in the same place of having particular characteristics in common is ………
Answers:
1. Democracy
2. Vedic
3. India
4. Democracy Quasi Federal
5. Lok Sabha and Rajya Sabha
6. Community

III. Match the following.

Answers:
1. (d)
2. (e)
3. (a)
4. (b)
5. (c)

IV. Give short answers.

Question 1.
What do you mean by “Republic”?
Answer:
A state in which supreme power is held by the people and their elected representatives and which has an elected (or) nominated President rather than a Monarch. e.g., India, Australia.

Question 2.
What is Democracy?
Answer:

1. Democracy is a form of government that allows people to choose their rulers.
2. Only leaders elected by people should rule the country.
3. People have freedom to express views, freedom to organise and freedom to protest.

Question 3.
Mention the salient features of Democracy.
Answer:

1. Elected representatives of people and final decision-making power to the representatives.
2. Free and fair elections.
3. Universal adult franchise with each vote having equal value.
4. Fundamental rights and protection of individual freedom.

V. Answer in detail.

Question 1.
Though democracy in India has been appreciated worldwide for its working there is still a lot of scope for improvement – Discuss.
Answer:
Though democracy in India has been appreciated worldwide for its working, there is still a lot of scope for improvement. The above-mentioned steps must be taken to ensure smooth functioning of democracy in the country.

Indian democracy can be successful and vibrant only when its citizens imbibe and reflect in their behavior the basic democratic values like equality, freedom, social justice, accountability and respect for all. Their mindset, thinking and behavior are expected to be in tune with the essential conditions of democracy. They have to appreciate the opportunities for their desired roles like participation, making the system accountable, fulfilling obligations, and playing proactive roles to actualize the goals of democracy.

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Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 2 Numbers and Sequences Ex 2.1

Exercise 2.1 Class 10 Maths Samacheer Question 1.
Find all positive integers which when divided by 3 leaves remainder 2.
Answer:
The positive integers when divided by 3 leaves remainder 2.
By Euclid’s division lemma a = bq + r, 0 ≤ r < b.
Here a = 3q + 2, where 0 ≤ q < 3, a leaves remainder 2 when divided by 3.
∴ 2, 5, 8, 11 ……………..

10th Maths Exercise 2.1 Samacheer Kalvi Question 2.
A man has 532 flower pots. He wants to arrange them in rows such that each row contains 21 flower pots. Find the number of completed rows and how many flower pots are left over?
Answer:
Here a = 532, b = 21
Using Euclid’s division algorithm
a = bq + r
532 = 21 × 25 + 7
Number of completed rows = 21
Number of flower pots left over = 7

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Ex 2.1 Class 10 Samacheer Question 3.
Prove that the product of two consecutive positive integers is divisible by 2.
Solution:
Let n – 1 and n be two consecutive positive integers. Then their product is (n – 1)n.
(n – 1)(n) = n² – n.
We know that any positive integer is of the form 2q or 2q + 1 for some integer q. So, following cases arise.
Case I. When n = 2q.
In this case, we have
n² – n = (2q)² – 2q = 4q² – 2q = 2q(2q – 1)
⇒ n² – n = 2r, where r = q(2q – 1)
⇒ n² – n is divisible by 2.

Case II. When n = 2q + 1
In this case, we have
n² – n = (2q + 1)² – (2q + 1)
= (2q + 1)(2q + 1 – 1) = 2q(2q + 1)
⇒ n² – n = 2r, where r = q (2q + 1).
⇒ n² – n is divisible by 2.
Hence, n² – n is divisible by 2 for every positive integer n.
Hence it is Proved

10th Maths Exercise 2.1 Question 4.
When the positive integers a, b and c are divided by 13, the respective remainders are 9,7 and 10. Show that a + b + c is divisible by 13.
Answer:
Let the positive integer be a, b, and c
We know that by Euclid’s division lemma
a = bq + r
a = 13q + 9 ….(1)
b = 13q + 7 ….(2)
c = 13q + 10 ….(3)
Add (1) (2) and (3)
a + b + c = 13q + 9 + 13q + 7 + 13q + 10
= 39q + 26
a + b + c = 13 (3q + 2)
This expansion will be divisible by 13
∴ a + b + c is divisible by 13

10th Maths 2.1 Exercise Question 5.
Prove that square of any integer leaves the remainder either 0 or 1 when divided by 4.
Solution:
Let x be any integer.
The square of x is x².
Let x be an even integer.
x = 2q + 0
then x² = 4q² + 0
When x be an odd integer
When x = 2k + 1 for some interger k.
x² = (2k + 1 )²
= 4k² + 4k + 1
= 4k (k + 1) + 1
= 4q + 1
where q = k(k + 1) is some integer.
Hence it is proved.

10th Maths Exercise 2.1 In Tamil Question 6.
Use Euclid’s Division Algorithm to find the Highest Common Factor (H.C.F) of
(i) 340 and 412
Answer:
To find the HCF of 340 and 412 using Euclid’s division algorithm. We get
412 = 340 × 1 + 72
The remainder 72 ≠ 0
Again applying Euclid’s division algorithm to the division of 340
340 = 72 × 4 + 52
The remainder 52 ≠ 0
Again applying Euclid’s division algorithm to the division 72 and remainder 52 we get
72 = 52 × 1 + 20
The remainder 20 ≠ 0
Again applying Euclid’s division algorithm
52 = 20 × 2 + 12
The remainder 12 ≠ 0
Again applying Euclid’s division algorithm
20 = 12 × 1 + 8
The remainder 8 ≠ 0
Again applying Euclid’s division algorithm
12 = 8 × 1 + 4
The remainder 4 ≠ 0
Again applying Euclid’s division algorithm
8 = 4 × 2 + 0
The remainder is zero
∴ HCF of 340 and 412 is 4

(ii) 867 and 255
Answer:
To find the HCF of 867 and 255 using
Euclid’s division algorithm. We get
867 = 255 × 3 + 102
The remainder 102 ≠ 0
Using Euclid’s division algorithm
255 = 102 × 2 + 51
The remainder 51 ≠ 0
Again using Euclid’s division algorithm
102 = 51 × 2 + 0
The remainder is zero
∴ HCF = 51
∴ HCF of 867 and 255 is 51

(iii) 10224 and 9648
Answer:
Find the HCF of 10224 and 9648 using Euclid’s division algorithm. We get
10224 = 9648 × 1 + 576
The remainder 576 ≠ 0
Again using Euclid’s division algorithm
9648 = 576 × 16 + 432
The remainder 432 ≠ 0
Using Euclid’s division algorithm
576 = 432 × 1 + 144
The remainder 144 ≠ 0
Again using Euclid’s division algorithm
432 = 144 × 3 + 0
The remainder is 0
∴ HCF = 144
The HCF of 10224 and 9648 is 144

(iv) 84,90 and 120
Answer:
Find the HCF of 84, 90 and 120 using Euclid’s division algorithm
90 = 84 × 1 + 6
The remainder 6 ≠ 0
Using Euclid’s division algorithm
4 = 14 × 6 + 0
The remainder is 0
∴ HCF = 6
The HCF of 84 and 90 is 6
Find the HCF of 6 and 120
120 = 6 × 20 + 0
The remainder is 0
∴ HCF of 120 and 6 is 6
∴ HCF of 84, 90 and 120 is 6

Numbers And Sequences 10th Class Question 7.
Find the largest number which divides 1230 and 1926 leaving remainder 12 in each case.
Solution:
The required number is the H.C.F. of the numbers.
1230 – 12 = 1218,
1926 – 12 = 1914
First we find the H.C.F. of 1218 & 1914 by Euclid’s division algorithm.
1914 = 1218 × 1 + 696
The remainder 696 ≠ 0.
Again using Euclid’s algorithm
1218 = 696 × 1 + 522
The remainder 522 ≠ 0.
Again using Euclid’s algorithm.
696 = 522 × 1 + 174
The remainder 174 ≠ 0.
Again by Euclid’s algorithm
522 = 174 × 3 + 0
The remainder is zero.
∴ The H.C.F. of 1218 and 1914 is 174.
∴ The required number is 174.

10th Maths Ex 2.1 Question 8.
If d is the Highest Common Factor of 32 and 60, find x and y satisfying d = 32x + 60y.
Answer:
Find the HCF of 32 and 60
60 = 32 × 1 + 28 ….(1)
The remainder 28 ≠ 0
By applying Euclid’s division lemma
32 = 28 × 1 + 4 ….(2)
The remainder 4 ≠ 0
Again by applying Euclid’s division lemma
28 = 4 × 7 + 0….(3)
The remainder is 0
HCF of 32 and 60 is 4
From (2) we get
32 = 28 × 1 + 4
4 = 32 – 28
= 32 – (60 – 32)
4 = 32 – 60 + 32
4 = 32 × 2 -60
4 = 32 x 2 + (-1) 60
When compare with d = 32x + 60 y
x = 2 and y = -1
The value of x = 2 and y = -1

10th Samacheer Maths Exercise 2.1 Question 9.
A positive integer when divided by 88 gives the remainder 61. What will be the remainder when the same number is divided by 11?
Solution:
Let a (+ve) integer be x.
x = 88 × y + 61
61 = 11 × 5 + 6 (∵ 88 is multiple of 11)
∴ 6 is the remainder. (When the number is divided by 88 giving the remainder 61 and when divided by 11 giving the remainder 6).

10th Maths 2.1 Question 10.
Prove that two consecutive positive integers are always coprime.
Answer:

1. Let the consecutive positive integers be x and x + 1.
2. The two number are co – prime both the numbers are divided by 1.
3. If the two terms are x and x + 1 one is odd and the other one is even.
4. HCF of two consecutive number is always 1.
5. Two consecutive positive integer are always coprime.

Fundamental Theorem of Arithmetic
Every composite number can be written uniquely as the product of power of prime is called fundamental theorem of Arithmetic.

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Tamilnadu Samacheer Kalvi 7th Tamil Solutions Term 2 Chapter 1.5 இலக்கியவகைச் சொற்கள்

மதிப்பீடு

சரியான விடையைத் தேர்ந்தெடுத்து எழுதுக.

Question 1.
எல்லார்க்கும் எளிதில் பொருள் விளங்கும் சொல் ……………..
அ) இயற்சொல்
ஆ) திரிசொல்
இ) திசைச்சொல்
ஈ) வடசொல்
Answer:
அ) இயற்சொல்

Question 2.
பலபொருள் தரும் ஒரு சொல் என்பது ……………………..
அ) இயற்சொல்
ஆ) திரிசொல்
இ) திசைச்சொல்
ஈ) வடசொல்
Answer:
ஆ) திரிசொல்

Question 3.
வடமொழி என்று அழைக்கப்படும் மொழி …………………………..
அ) மலையாளம்
ஆ) கன்ன டம்
இ) சமஸ்கிருதம்
ஈ) தெலுங்கு
Answer:
இ) சமஸ்கிருதம்

பொருத்துக

1. இயற்சொல் – பெற்றம்
2. திரிசொல் – இரத்தம்
3. திசைச்சொல் – அழுவம்
4. வடசொல் – சோறு
Answer:
1. இயற்சொல் – சோறு
2. திரிசொல் – அழுவம்
3. திசைச்சொல் – பெற்றம்
4. வடசொல் – இரத்தம்

குறுவினா

Question 1.
மண், பொன் என்பன எவ்வகைச் சொற்கள்?
Answer:

• எளிதில் பொருள் விளங்கும் வகையில் அமைந்த சொற்கள் இயற்சொற்கள் எனப்படும்.
• இயற்சொல் பெயர், வினை, இடை, உரி ஆகிய நான்கு வகையிலும் வரும்.
• மண், பொன் – பெயர் இயற்சொல்

Question 2.
இயற்சொல்லின் நான்கு வகைகள் யாவை?
Answer:
இயற்சொல்லின் நான்கு வகைகள்.
இயற்சொல் பெயர், வினை, இடை, உரி ஆகியன நான்கு வகைகளாகும்.

எடுத்துக்காட்டு :
மண், பொன் – பெயர் இயற்சொல்
நடந்தான், வந்தான் – வினை இயற்சொல் அவனை,
அவனால் – இடை இயற்சொல்
மாநகர் – உரி இயற்சொல்

Question 3.
குங்குமம், கமலம் என்பன எவ்வகை வடசொற்கள்?
Answer:
கமலம், குங்குமம் என வடமொழியில் இருப்பது போன்றே தமிழில் எழுதுவதைத் தற்சமம் என்பர்.

சிறுவினா

Question 1.
இலக்கிய வகைச் சொற்கள் எத்தனை வகைப்படும்? அவை யாவை?
Answer:
இலக்கிய வகைச் சொற்கள் நான்கு வகைப்படும்

1. இயற்சொல்,
2. திரிசொல்,
3. திசைச்சொல்,
4. வடசொல்

(i) இயற்சொல் : எளிதில் பொருள் விளங்கும் வகையில் அமைந்த சொற்கள் இயற்சொற்கள் எனப்படும். எடுத்துக்காட்டு : கடல், கப்பல்

(ii) திரிசொல் : கற்றோருக்கு மட்டுமே விளங்குவதாகவும் இலக்கியங்களில் மட்டுமே பயின்று வருபவையாகவும் அமையும் சொற்கள் திரிசொற்கள் எனப்படும். எடுத்துக்காட்டு : வங்கூழ், அழுவம்.

(iii) திசைச்சொல் : வடமொழி தவிர, பிறமொழிகளில் இருந்து வந்து தமிழில் இடம்பெறும் சொற்கள் திசைச்சொற்கள் எனப்படும். எடுத்துக்காட்டு: சாவி, சன்னல்.

(iv) வடசொல் : வடமொழியிலிருந்து வந்து தமிழில் இடம் பெறும் சொற்கள் வடசொற்கள் எனப்படும். எடுத்துக்காட்டு: வருடம், மாதம்.

Question 2.
திரிசொல்லின் வகைகள் குறித்து விளக்குக.
Answer:
திரிசொல்லின் வகைகள் :
திரிசொற்களை ஒரு பொருள் குறித்த பல திரிசொற்கள் எனவும். பல பொருள் குறித்த ஒரு திரிசொல் எனவும் இருவகைப்படுத்தலாம்.

ஒரு பொருள் குறித்த பல திரிசொற்கள்
எடுத்துக்காட்டு :
வங்கம், அம்பி, நாவாய் – என்பன கப்பல் என்னும் ஒரே பொருளைத் தருவதால் ஒரு பொருள் குறித்த பல திரிசொற்கள் என்பர்.

பல பொருள் குறித்த ஒரு திரிசொல் :
எடுத்துக்காட்டு :
இதழ் என்னும் சொல் பூவின் இதழ், உதடு, கண்ணிமை, பனையேடு, நாளிதழ் ஆகிய பல பொருள்களைத் தருவதால் பலபொருள் குறித்த ஒரு திரிசொல் என்பர்.

Question 3.
பண்டிகை, கேணி என்பன எவ்வகைச் சொற்கள்? விளக்குக.
Answer:

• பண்டிகை, கேணி என்பன திசைச் சொற்களாகும்.
• வடமொழி தவிர, பிற மொழிகளில் இருந்து வந்து தமிழில் இடம்பெறும் சொற்கள் திசைச் சொற்கள் எனப்படும்.
• முற்காலத்தில் பாண்டி நாட்டைத் தவிர, தமிழ்நாட்டின் பிற பகுதிகளில் வழங்கிய கேணி (கிணறு, பெற்றம் (பசு) போன்ற சொற்களையும் திசைச்சொற்கள் என்றே வழங்கினர்.

கற்பவை கற்றபின்

Question 1.
நாளிதழ் செய்தியொன்றை எடுத்துக் கொண்டு அதில் உள்ள நால்வகைச் சொற்களையும் வகைப்படுத்திப் பட்டியல் உருவாக்குக.
Answer:
(i) வீடுகளிலே நடைபெறும் விஷேசங்களின் போது, வெளியூர்கள் சென்று திரும்பும் போது, பரிசளிப்புகள் நடத்தும் போதும் புத்தகங்கள் வாங்குவது என்று ஒரு – பழக்கத்தைக் கொஞ்சம் வசதியுள்ள வீட்டார் சில காலத்துக்காவது ஏற்படுத்திக் கொண்டால் சுலபத்தில் ஒரு சில புத்தகசாலையை அமைத்து விடலாம்.
விசேஷம் – சிறப்பு
விசேஷம் – வடமொழி

(ii) சன்னல் வழியாக இராமு போவதை கோபு பார்த்துக் கொண்டிருந்தான்.
சன்னல் – சாளரம்
சன்னல் – திசைச் சொல்

(iii) நாவாய் கரையோரம் ஒதுங்கியது
நாவாய் – திரிசொல்
நாவாய் – கப்பல்

(iv) கபிலன் கதை எழுதினான்
எழுதினான் – வினை இயற்சொல்.

கூடுதல் வினாக்கள்

நிரப்புக.

Question 1.
ஓர் எழுத்து தனித்தும் ஒன்றிற்கும் மேற்பட்ட எழுத்துகள் தொடர்ந்தும் வந்து பொருள் தருவது ………………. எனப்ப டும்.
Answer:
சொல்

Question 2.
சொல் என்னும் பொருள் தரும் வேறு சொற்கள் ……….
Answer:
பதம், மொழி, கிளவி

Question 3.
இலக்கண முறைப்படி …………….. எனச் சொற்கள் நான்கு வகைப்படும்.
Answer:
பெயர்ச்சொல், வினைச்சொல், இடைச்சொல், உரிச்சொல்

Question 4.
இலக்கிய வகைச் சொற்களை …………….. என நான்கு வகையாகப் பிரிக்கலாம்.
Answer:
இயற்சொல், திரிசொல், திசைச்சொல், வடசொல்

Question 5.
எளிதில் பொருள் விளங்கும் வகையில் அமைந்த சொற்கள் …………… எனப்படும்.
Answer:
இயற்சொற்கள்

Question 6.
இயற்சொல் ……………………… ஆகிய நான்கு வகையிலும் வரும்.
Answer:
பெயர், வினை, இடை, உரி

Question 7.
கற்றோர்க்கு மட்டுமே விளங்கும் சொற்கள் …………… எனப்படும்.
Answer:
திரிசொற்கள்

Question 8.
லக்ஷ்மி என்பதை இலக்குமி என்றும், விஷம் என்பதை விடம் என்றும் தமிழ் எழுத்துகளால் மாற்றி எழுதுவதை ………….. என்பர்.
Answer:
தற்பவம்

Question 9.
வடசொற்களை ………………… என இருவகையாகப் பிரிப்பர்.
Answer:
தற்சமம், தற்பவம்

Question 10.
திரிசொல் …………………………………………………. ஆகிய நான்கு வகையிலும் வரும்.
Answer:
பெயர், வினை, இடை, உரி

மொழியை ஆள்வோம்

கேட்க

Question 1.
கடற்பயணம் தொடர்பான கதைகளைப் பெற்றோரிடம் கேட்டு மகிழ்க.
Answer:
சாகச கடல் பயணம்
மாலை வேளை வானம் மேகம் சூழ்ந்தது. நள்ளிரவைப் போல் வானம் இருண்டு காணப்பட்டது. ஆனால் இன்னும் சூரியன் மறையவில்லை. புயல் மழை கொட்டுவதற்கான அறிகுறிகள் தெரிந்தன. கடல் அலைகள் ஆர்ப்பாட்டம் இல்லாமல் ஒரு பனை மர அளவிற்கு ஏறி இறங்கின. அதில் பனை மலர்’ என்ற கப்பல் ராட்டினம் போல மேலே ஏறி கீழே இறங்கியது.

பனை மலர் கப்பல் தமிழ்நாட்டின் தரங்கம்பாடி துறைமுகத்திலிருந்து கிளம்பி ஒரு மாதத்துக்கும் மேலாகிறது. இங்கிருந்து கப்பல் நிறைய ஏலம், கிராம்பு, மிளகு, பட்டை, சோம்பு, ஜாதி, பத்திரி போன்ற உணவுக்கு நல்ல வாசனை தரும் ஏராளமான பொருட்கள், தூத்துக்குடி முத்துக்கள், பவளங்கள், மாணிக்கக் கற்கள், பட்டுச் சேலைகள், பருத்தி துணிகள், சிற்பங்கள், கைவினைப் பொருட்கள் போன்ற பலவகையான பொருட்களை ஏராளமாக ஏற்றிச் சென்றனர்.

கப்பலில் ஆறு மாதங்களுக்குத் தேவையான தண்ணீர், உப்பு, அரிசி, மிளகாய், எண்ணெய் போன்றவற்றை சேமித்துக் கொண்டு போயிருந்தனர். இப்போது, இலங்கையைத் தாண்டி 300 ஆவது கடல் மைல் தொலைவில் பெரும் புயல் ஒன்றை எதிர்கொண்டுள்ளனர். முதலில் சாதாரணமாக நினைத்தாலும், காற்று சுழற்றும், சுழற்றலில், கப்பல் உடைந்து தூள்தூளாகப் போகிறது எனப் பயந்தார்கள். ஆனால் கப்பல் மேலும் கீழும் குதித்தது. கிறுகிறுவென சுற்றிச் சுழன்றது.

கடல் நீர் அருவி கொட்டுவதைப் போல கப்பலுக்குள் புகுந்தது. சில நிமிடங்களில் புயல் நின்று விட்டது. ஊழியர்கள் நூறு பேரும் கப்பலில் புகுந்த தண்ணீரை வாரி வாரி இறைத்து கடலில் ஊற்றினர்.

இரவில் வானத்திலிருந்து சில சமயங்களில் சின்னச் சின்ன எரிகற்கள் விழும். கடலுக்கு மேலே வரும் திமிலங்கள் மிகப்பெரியவை. அவை மேலே வரும் போது அவற்றின் உடல் ஒரு பெரிய விளையாட்டு மைதானம் கடலில் இருப்பதைப் போல தெரியும். அதைப் பார்த்ததும் கப்பல் ஊழியர்கள் அதை நிலம் என நினைத்துக்கொண்டு கடலில் பாய பரபரப்பார்கள். ஆனால் மாலுமி அவர்களை அதட்டி நிறுத்துவார்.

கடலுக்குள் மின்னலைப் போல தெரியும் அபூர்வ உயிரினங்கள், கண்ணைப் பறிக்கும் வண்ணங்களில் படர்ந்திருக்கும் கடற்கொடிகள், வலையை வீசினால் இரண்டு கப்பல்கள் நிறையும் அளவுக்கு வரும் மீன் கூட்டங்கள் என்றெல்லாம் பார்த்தாலும் அவர்களுக்கு சலிப்பாய் இருந்தது. எப்போது நிலத்தைப் பார்ப்போம் என ஏங்கிப் போனார்கள்.

இப்படியாக பயணம் செய்து ஒரு வழியாக அவர்கள் ஏதென்ஸ் நகரத்தின் 9 துறைமுகத்துக்கு வந்து சேர்ந்தார்கள். கொண்டு வந்த பொருட்கள் எல்லாவற்றையும் கிடங்கில் இறக்கி வைத்தார்கள். அப்போதே நூற்றுக்கணக்கானவர்கள் அவர்களை .8 மொய்த்துக் கொண்டார்கள். ஒவ்வொரு பொருளையையும் பார்த்து வாயைத் திறந்து 3 ஆச்சரியத்தில் மூழ்கினர் அங்குள்ளோர்.

முறைப்படி மன்னரைச் சந்தித்த பின்தான் வியாபாரத்தைத் தொடங்க வேண்டும் என்பதில் மாலுமி உறுதியாக இருந்தார். ஏதென்சின் ராணி பாட்ரியா அவர்களை வரவேற்றார் மாலுமி: அவர்கள் கொண்டு வந்த பொருட்களில் பாதியை ராணி பாட்ரியா வாங்கிக் கொண்டார். அரண்மனையை ஏராளமான தமிழக கலைப் பொருட்களைக் கொண்டு தமிழ்நாட்டின் அரண்மனையைப் போன்று மாலுமி அலங்கரித்தார்.

ராணி மிகவும் மகிழ்ச்சி அடைந்து ஆப்பிரிக்க வைரங்கள் பதித்த பெரிய வைர் மாலையை மாலுமிக்கு பரிசளித்தார். மீண்டும் விரைவிலேயே அதிக பொருட்களோடு வர வேண்டும் எனக் கேட்டுக் கொண்டார்.

அதன் பிறகு மாலுமி மற்றும் கப்பல் ஊழியர்கள் துறைமுகத்திலேயே ஒரு மாதம் 3 தங்கியிருந்து மீதமிருந்த பொருட்களை விற்றனர். கப்பல் ஊழியர்கள் கலைநயத்துடன் 3 இருந்த ஏதென்ஸ் வீதிகளில் மகிழ்ச்சியுடன் தினமும் சுற்றி வந்தனர். கடற்கரையில் இ விளையாடி மகிழ்ந்தனர். ஒரு மாதம் கழித்து இந்தியாவுக்கு திரும்ப மாலுமி முடிவு செய்தார்.

ராணி மினு… மினு…. என சில முறை குரல் கொடுத்தார். மினு நான் வளர்க்கும் டால்பின் உங்களுடன் உங்கள் நாடு வரை துணைக்கு வரும் என்றார். டால்பின் இவர்களின் கடற்பயணத்திற்கு உறுதுணையாக இருந்தது.

பின்வரும் தலைப்பில் இரண்டு நிமிடம் பேசுக

கப்பல்களின் வகைகளும் பயன்களும்.
Answer:
வணக்கம்!
நீர்வழிப்பயணத்தை இரண்டு வகையாகப் பிரிக்கலாம்.

1. உள்நாட்டு நீர்வழிப் பயணம், 2. கடல்வழிப் பயணம்

கப்பல் பயணம் : காற்றின் துணை கொண்டு கப்பலைச் செலுத்திய நம் முன்னோரின் திறமையைச் சங்கப்பாடல்கள் மூலம் தெரிந்து கொள்ள முடிகிறது. கப்பல்கள் மூலம் பொருள்கள் பூம்புகார் துறைமுகத்தின் வாயிலாக ஏற்றுமதி இறக்குமதி செய்யப்பட்டன என்பதற்கு ஆதாரமாக பட்டினப்பாலை என்னும் நூலின் மூலம் தெரிந்து கொள்ளலாம். கப்பல் வகைகள் : ‘உலகு கிளர்ந்தன்ன உருகெழு வங்கம்’ என்று பெரிய கப்பலை அகநானூறு குறிப்பிடுகிறது. ‘அருங்கலம் தரீஇயர் நீர்மிசைநிவக்கும் பெருங்கலி வங்கம் என்று பதிற்றுப்பத்து குறிப்பிடுகிறது. சேந்தன் திவாகரம் என்னும் நிகண்டு நூலில் பலவகையான கப்பலின் பெயர்கள் குறிப்பிடப்பட்டுள்ளன.

சிறிய நீர் நிலைகளைக் கடக்க தோணி, ஓடம், படகு, புணை, மிதவை, தெப்பம் ஆகியவற்றை தமிழர்கள் பயன்படுத்தினர். கலம், வங்கம். நாவாய் முதலியவை அளவில் பெரியவை. இவற்றைக் கொண்டு தமிழர்கள் கடல்பயணம் மேற்கொண்டனர். கப்பலின் பயன்கள் : முற்காலத்தில் மக்கள் பயணம் செய்வதற்கும் மட்டும் அன்றிப் போர் புரியவும் கப்பல் பெரிதும் பயன்பட்டது. இக்காலத்தில் பெரும்பாலும் பொருள்களை ஏற்றிச் செல்லவே கப்பல்கள் பயன்படுத்தப்படுகின்றன. அவற்றைச் சரக்குக் கப்பல்கள் என்பர். போருக்குப் பயன்படும் பெரிய கப்பல்களும் இன்று உள்ளன.

சொல்லக் கேட்டு எழுதுக

1. பெருந்திரளான மக்களையும் பொருள்களையும் கப்பல்கள் ஏற்றிச் செல்லும்.
2. காற்றின் உதவியால் செலுத்தப்படுபவை பாய்மரக் கப்பல்கள்
3. வானில் தோன்றும் விண்மீன்களின் நிலையை வைத்துத் திசையை அறிவர்.
4. ஆழ்கடல் விந்தைகளைப் பற்றி ஆய்வுகள் செய்தார்.
5. நார்வே நாட்டின் கடற்கரையில் கண்விழித்தோம்.

அறிந்து பயன்படுத்துவோம்

காலம் மூன்று வகைப்படும்.
அவை: 1. இறந்தகாலம், 2. நிகழ்காலம், 3. எதிர்காலம்.
இறந்தகாலம் : நடந்த செயலைக் குறிப்பது இறந்தகாலம்.
எடுத்துக்காட்டு: பார்த்தான். ஆடினாள், பறந்தது.

• கபிலன் திரைப்படத்தைப் பார்த்தான்.
• கோதை நடனம் ஆடினாள்
• கிளி பறந்தது.

நிகழ்காலம் : நடக்கும் செயலைக் குறிப்பது நிகழ்காலம்.
எடுத்துக்காட்டு : பார்க்கிறான், ஆடுகின்றாள், பறக்கின்றது.

• கலிவரதன் நாடகத்தைப் பார்க்கிறான்.
• பூங்குழலி நாட்டியம் ஆடுகின்றாள்.
• பறவை வானில் பறக்கின்றது.

எதிர்காலம் : நடக்கவிருக்கும் செயலைக் குறிப்பது எதிர்காலம்.
எடுத்துக்காட்டு : காண்பான், ஆடுவாள், பறக்கும்.

• திருவண்ணாமலை தீபத்தை மணிமாறன் கண்களால் காண்பான்.
• வண்டார்குழிலி ஆட்டம் ஆடுவாள்.
• வண்டு பறக்கும்.

கட்டங்களை நிரப்புக

Answer:

பொருத்தமான காலம் அமையுமாறு திருத்தி எழுதுக

Question 1.
அமுதன் நேற்று வீட்டுக்கு வருவான்.
Answer:
அமுதன் நேற்று வீட்டுக்கு வந்தான்

Question 2.
கண்மணி நாளை பாடம் படித்தாள்.
Answer:
கண்மணி நாளை பாடம் படிப்பாள்

Question 3.
மாடுகள் இப்பொழுது புல் மேயும்
Answer:
மாடுகள் இப்பொழுது புல் மேய்கின்றன.

Question 4.
ஆசிரியர் நாளை சிறுதேர்வு நடத்தினார்.
Answer:
ஆசிரியர் நாளை சிறுதேர்வு நடத்துவார்.

Question 5.
நாங்கள் நேற்றுக் கடற்கரைக்குச் செல்கிறோம்.
Answer:
நாங்கள் நேற்றுக் கடற்கரைக்குச் சென்றோம்.

கொடுக்கப்பட்டுள்ள குறிப்புகளைக் கொண்டு கட்டுரை எழுதுக

பயணங்கள் பலவகை

முன்னுரை – பயணத்தின் தேவை – தரைவழிப்பயணம் – கடல்வழிப்
பயணம் – வான்வழிப்
பயணம் – முடிவுரை

முன்னுரை:
பயணம் செய்வதில் இளஞ்சிறார்கள் முதல் முதியவர்கள் வரை பெருவிருப்பம் கொள்வார்கள். பயணம் தரைவழிப் பயணம், நீர்வழிப் பயணம், வான்வழிப் பயணம் என மூன்று வகையாகப் பிரிக்கலாம். இவற்றைப் பற்றி இங்கு ஆய்வு செய்வதே இக்கட்டுரையின் நோக்கமாகும்.

பயணத்தின் தேவை :
திரைகடல் ஓடியும் திரவியம் தேடு . இது ஔவை சொன்ன அமுதமொழி. சுற்றுப்பயணம் மேற்கொண்டால் பல நாடுகளைப் பார்க்கலாம். அங்குள்ள கலைநயம் மிக்க சிற்பங்கள், கோயில்கள், இயற்கைக் காட்சிகள், கவின்மிகு கலைப்பொருட்கள் இவற்றினைக் கண்டு ரசிக்கலாம்.

தொழில் நிமித்தமாக பயணம் மேற்கொள்வதும் அங்குள்ள மக்களின் பழக்க வழக்கங்களையும் கலாச்சாரங்களையும் பற்றியும் அறிவுப்பூர்வமாக தெரிந்து கொள்ளலாம்.

தரைவழிப் பயணம்:
ஓரிடத்திலிருந்து மற்றோர் இடத்திற்கு பயணிப்பது பயணம் ஆகும். பேருந்து, சிற்றுந்து, மகிழுந்து, இரு சக்கர வாகனம் இவற்றின் மூலம் பயணம் செய்வது தரைவழிப் பயணம் ஆகும். தரைவழிப் பயணம் ஏழை எளியவர், நடுத்தர வகுப்பினர், உயர் தர வகுப்பினர் யாவரும் பயன்படுத்தும் பயணம் ஆகும். போக்குவரத்து நெரிசல் அதிகம் ஏற்படுவதால் இப்பயணத்தில் நேரம் விரயமாகிறது. மன உளைச்சல்களுக்கு ஆளாக வேண்டிய சூழல் ஏற்படுகிறது.

கடல்வழிப் பயணம்:
வானூர்திகள் கண்டுபிடிக்கப்படாத காலத்தில் வெளிநாட்டுப் பயணத்திற்கு உதவியவை கப்பல்களே. கப்பல்கள் மூலம் பொருட்கள் துறைமுகத்திலிருந்து ஏற்றுமதி இறக்குமதி செய்யப்பட்டன. இதற்கான ஆதாரங்கள் பட்டினப்பாலையில் தரப்பட்டுள்ளன. தோணி, ஓடம், படகு, புணை, மிதவை, தெப்பம் போன்றவற்றை சிறிய நீர்நிலைகளைக் கடக்கப் பயன்படுத்தினர். கலம், வங்கம், நாவாய் முதலியவை அளவில் பெரியவை. இவற்றைக் கொண்டு தமிழர்கள் கடல்பயணம் மேற்கொண்டனர். கடலில் செல்லும் கப்பல்களுக்குத் துறைமுகம் இருக்கும் இடத்தைக் காட்டுவதற்காக அமைக்கப்படுவது கலங்கரை விளக்கம் ஆகும்.

வான்வழிப் பயணம்:
மிக துரிதமாக ஓரிடத்திலிருந்து மற்றோர் இடத்திற்குக் கொண்டு சேர்ப்பது வான்வழிப்பயணமே. வான்வழிப் பயணம் வந்த பிறகு கடல் வழிப்பயணம் குறைந்தது. கடல் வழிப் பயணத்தில் போக வேண்டிய இடத்திற்கு சில நாட்கள் ஆகும். வான்வழிப் பயணம் மூலமாக சில மணி நேரங்களில் போக வேண்டிய இடத்திற்கு போய் சேரலாம். மிக முக்கியமான அரசியல் பிரமுகர்கள், அரசுத் துறையில் இருப்பவர்கள், வியாபாரிகள்; தொழிலதிபர்கள் போன்றோர் வேலை நிமித்தமாக இந்த வான்வழிப் பயணத்தை மேற்கொள்கின்றனர்.

முடிவுரை:
பயணம் மனிதர்கள் வாழ்க்கையில் அன்றாடம் வந்து போகும் முக்கிய நிகழ்வு ஆகும். தரைவழிப் பயணத்தை யாவரும் பயன்படுத்துவர். கடல்வழிப்பயணத்தில் கனரகப் பொருள்களை ஏற்றிச் செல்ல கப்பல்கள் பயன்படுகின்றன. தொழில் ரீதியாக வான்வழிப் பயணத்தைச் சிலர் பயன்படுத்துகின்றனர்.

மொழியோடு விளையாடு

குறுக்கெழுத்துப் புதிர்.

பிறமொழிச் சொற்களுக்கு இணையான தமிழ்ச் சொற்களை அறிவோம்.

Answers:

இடமிருந்து வலம் 1. தந்தை , 2. அறிவியல், 4. தேர்வு, 19. குறிக்கோள்
மேலிருந்து கீழ் 1. தலைவர், 3. வியப்பு, 7. தொடக்கம், 12. நூறு
வலமிருந்து இடம் : 6. இடர், 8. உடல், 13. வரலாறு, 14. ஓசை
கீழிருந்து மேல் 5. முதல், 9. கட்டளை , 11. நாள், 15. மகிழ்ச்சி

கட்டங்களை நிரப்புக

குறிப்புகளை கொண்டு ‘மா’ என்னும் எழுத்தில் தொடங்கும் சொற்களைக் கண்டறிந்து கட்டங்களை நிரப்புக.

நிற்க அதற்குத் தக

என் பொறுப்புகள்

1. கடல் மற்றும் கடற்கரையின் தூய்மை காப்பேன்.
2. சுற்றுச்சூழலுக்குத் தீங்கு தராத பொருள்களையே பயன்டுத்துவேன்.

கலைச்சொல் அறிவோம்

You can Download Samacheer Kalvi 9th Social Science Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th Social Science Geography Solutions Chapter 1 Lithosphere – I Endogenetic Processes

Lithosphere – I Endogenetic Processes Textual Exercise

I. Choose the correct answer.

Lithosphere 1 Endogenic Processes Question 1.
The ………….. is the rigid outer layer of the Earth.
(a) core
(b) mantle
(c) Crust
(d) inner core
Answer:
(c) Crust

Lithosphere Endogenic Process Question 2.
…………… layer is made up of liquid iron.
(a) Inner core
(b) Outer core
(c) Mantle
(d) Crust
Answer:
(b) Outer core

Samacheer Kalvi 9th Social Science Geography Chapter 1 Question 3.
Magma is found in the ……………
(a) crust
(b) mantle
(c) core
(d) None of the above
Answer:
(b) mantle

9th Social Guide Question 4.
Diastrophism is connected to ……………
(a) volcanism
(b) earthquakes
(c) tectonics
(d) fold/fault
Answer:
(c) tectonics

Samacheer Kalvi 9th Social Book Answers Question 5.
The movement of tectonic plates is induced by ………….. energy.
(a) hydel
(b) thermal
(c) wave
(d) tidal
Answer:
(b) thermal

Lithosphere 1 Endogenic Processes Answers Question 6.
In the ancient period, Gondwana land moved towards ………….. direction.
(a) north
(b) south
(c) east
(d) west
Answer:
(a) north

9th Social Science Guide Question 7.
Many million years ago, India was a part of the super continent ………….
(a) Gondwana
(b) Laurasia
(c) Panthalasa
(d) Pangea
Answer:
(a) Gondwana

Endogenetic Processes Match Question 8.
The movement of plates that creates stress and tension in the rocks causing them to stretch and cracks result in ………….
(a) fold
(b) fault
(c) mountain
(d) earthquake
Answer:
(b) fault

Social 9th Guide Question 9.
……………… refers to a bowl-shaped depression found at the top of the volcano.
(a) crater
(b) vent
(c) chamber
(d) volcanic cone
Answer:
(a) crater

9th Standard Social Guide Question 10.
The point of origin of an Earthquake is called the …………..
(a) epicentre
(b) focus
(c) seismic wave
(d) magnitude
Answer:
(a) epicentre

II. Match the following.

Answer:

III. Consider the given statements.

9 Social Guide Question 1.
(i) Mt. Fuji is a dormant Volcano.
(ii) Mt. Kilimanjaro is a dormant Volcano.
(iii) Mt. Tanzania is a dormant Volcano.
Which of the statement(s) is are true?
(a) (i) is true
(b) (ii) is true .
(c) (iii) is true
(d) (i) (ii) (iii) are true
Answer:
(a) (i) is true

9th Std Social Science Guide Pdf Question 2.
Statement: Magma gushes out when it finds vents.
Reason: Interior of the Earth contains compressed hot magma.
Which of the statement(s) is are true?
(a) Statement & reason are true
(b) Statement is true, reason is false
(c) Statement is false reason is true
(d) Statement & reason are false
Answer:
(a) is true

9std Social Guide Question 3.
Statement I: Mountain ranges are formed by the collision of tectonic plates.
Statement II: The movement of tectonic plates is due to the thermal energy from the mantle.
(a) Statement I is false II is true
(b) Statement I and II are false
(c) Statement I is true II is false
(d) Statement I and II are true
Answer:
(d) is true

IV. Answer the following in one or two sentences.

9th Standard Social Science Guide Pdf Question 1.
Write a brief note on the various spheres of the Earth.
Answer:
(i) The Earth is divided into Biotic and ABiotic Spheres.

(ii) Biotic sphere is the Biosphere
A Biotic sphere is further divided into Lithosphere, Atmosphere and Hydrosphere.

Social Guide For Class 9 Question 2.
Mention the layers of the interior of the Earth.
Answer:
The structure of the Earth’s interior is divided into three layers namely the crust, the mantle and the core.

Social Guide Question 3.
What is pedosphere?
Answer:
The ‘Pedosphere’ is part of the lithosphere made up of soil and dirt. It exists at the interface of lithosphere, atmosphere, hydrosphere and biosphere.

9th Social Book Back Answers Question 4.
Define Plate tectonics.
Answer:

1. The tectonic plates float independently.
2. Collisions of the tectonic plates produce mountain ranges and other irregular surface features both on land and the ocean floor. This phenomenon is called ‘Plate tectonics.’

9th Std Social Guide Question 5.
Write a note on Fold and fault?
Answer:
Folding: Due to lateral compressional forces, the plates are forced to move upwards and downwards. This is called‘Folding’.
Faulting: The movement of plates also create stress and tension in the rocks, causing them to stretch and crack. This called ‘faulting’.

Samacheer Kalvi Guru 9th Social Science Question 6.
What is Tsunami?
Answer:

• The word Tsunami is a Japanese term meaning harbour waves.
• It is adopted to describe large seismically generated sea waves caused by Earthquakes Submarine explosions and landslides.

Social Science 9th Guide Question 7.
What is a Volcano? Mention its major components.
Answer:
A volcano is a vent or an opening on the surface of the Earth’s crust through which hot solid, liquid and gaseous materials (Magma) erupt out to the surface from the Earth’s interior.

9th Guide Social Question 8.
What is an Earthquake and how it occurs?
Answer:
Earthquakes are generally caused by the sudden vibrations in the Earth’s crust which spreads outward in all directions as waves from the source of disturbance.

Samacheer Kalvi 9th Social Science Book Back Answers Question 9.
What are seismic waves and mention its types?
Answer:
Earthquakes generate seismic waves. The nature force and speed of these seismic waves depend on the nature of the medium through which it passes.
The major types are
(a) Primary (or) P waves
(b) Secondary (or) S waves
(c) Surface waves (or) L waves.

Question 10.
Write about the Pacific Ring of fire.
Answer:

• The Pacific Ring of fire is an arc around the Pacific Ocean where many volcanoes are found.
• The Pacific Ring of fire is the most seismically and volcanically active zone in the world.

V. Give Reasons for the following.

Question 1.
SIAL floats over SIMA.
Answer:

1. SIAL consists of Silica and Aluminium.
2. SIMA contains Silica and Magnesium.
3. SIAL is lighter than SIMA.
   Therefore SIAL floats over SIMA.

Question 2.
Igneous rocks are also called Primary Rocks or Mother rocks.
Answer:
Igneous rocks are also called Primary Rocks (or) Mother rocks because all other rocks are directly or indirectly formed from them.

VI. Distinguish between.

Question 1.
Core and crust.
Answer:

Question 2.
Epicentre and Hypocentre.
Answer:

Question 3.
Divergent and convergent boundaries.
Answer:

Question 4.
Primary waves and Secondary waves.
Answer:

Question 5.
Shield Volcano and Volcanic Dome.
Answer:

VII. Write answers in a Paragraph.

Question 1.
Describe the structure of the Earth.
Answer:
The outer surface and inner core of the Earth are totally different in their nature and structure. The structure of the Earth’s interior is divided into three layers namely the crust, the mantle and the core.

Crust: Crust is the outer layer of the Earth, where we live. It is the skin of our Earth, which ranges between 5 to 30 km. It is the solid and rigid layer of the Earth. The thickness of the crust is greater below the continents than the ocean floor. The crust is classified as continental crust and oceanic crust. The major elements of crust are Silica (Si) and Aluminium (Al) and thus, it is termed as SIAL.

Mantle: The interior part beneath the crust is called mantle, which is about 2,900 km thick. The major elements of the mantle are Silica (Si) and Magnesium (Mg) and hence it is also termed as SIMA. In the upper part of the mantle, the rock remains solid, whereas in the lower part of the mantle, rocks are in molten form. This molten rock inside the Earth is called ‘magma’.

Core: The core is the innermost and hottest layer of the Earth which lies below the mantle.
It is composed mainly of Nickel (Ni) and Iron (Fe). Hence it is called NIFE. The core is divided into Solid inner core and Liquid outer core. The presence of large quantities of iron in the core is responsible for the Earth’s gravitational force. As the Earth rotates on its axis, the liquid outer core spins over the solid inner core and generates the Earth’s magnetic field.
This is responsible for the functioning of the magnetic compass. Due to high pressure, the materials in the inner core are unable to move and hence remain solid.

Question 2.
Write a note on the internal and external processes of Earth.
Answer:
The formation and deformation of landforms on the surface of the Earth is a continuous activity of two broad processes i.e. internal and external. These processes cause stress and deformation on Earth materials and finally bring changes on the surface of the Earth. These are referred as Geomorphic Processes.

The forces that act from the Earth’s interior towards the Earth’s surface are called Internal processes or Endogenetic processes. These forces build the landscape and create topographic relief.

The forces that act on the surface of the Earth due to natural agents like running water, glacier, wind, waves etc. are called External processes or Exogenetic processes. These external processes tear the landscape down into relatively low elevated plains.

Question 3.
How are volcanoes classified based on the periodicity of their eruptions?
Answer:
Based on the periodicity of eruptions, volcanoes are classified into
(i) Active volcano,
(ii) Dormant volcano
(iii) Extinct volcano.
(i) Active Volcano: Active volcanoes are those which constantly eject volcanic lava, gases and fragmented materials. (e.g.) Mount St. Helens in the United States.

(ii) Dormant Volcano: Volcanoes that do not show any sign of volcanic activity for a long period of time are known as dormant volcanoes. Sometimes there may be a sudden explosion. which may cause unimaginable loss to life and property (e.g. ) Mt. Fuji, Japan.

(iii) Extinct or Dead Volcano: When a volcano permanently stops its volcanic activity, then it is called as extinct or dead volcano (e.g.) Mt. Kilimanjaro, Tanzania.
Volcanoes can also be classified based on their structure and composition as composite volcano, shield volcano and dome volcano.

Question 4.
Explain the effects of Volcanoes.
Answer:
Constructive Effects: Volcanic materials enrich the soil fertility that promotes agricultural activities. The hot volcanic region helps in generating geothermal energy. Many dormant and active volcanoes are the most attractive tourist spots of the world. Most of the volcanic materials are used as building materials.

Destructive Effects: Volcanic eruption causes Earthquakes, fast floods, mud slide and rock fall. Lava can travel very far and bum, bury, or damage anything in its path. The large amount of dust and ash makes breathing hard and irritable. Volcanic emptions can alter the weather conditions and disrupt transport (Iceland volcanic eruption) in and around the volcanic region.

VIII. Map Skill.

On the given outline map of the world, mark the following:
(a) Pacific Ring of fire
(b) Earthquake-prone zones (any two)
(c) Locate any two active volcanoes of the world
(d) Himalayas and Alps ranges
(e) Rift valley of East Africa
Answer:
(a) Pacific Ring of fire: It is a major area and an arc in the basin of the Pacific ocean where many earthquakes and volcanic emptions occur.

(b) Earthquake prone zones (any two): Turkey, Indonesia

(c) Locate any two active volcanoes of the world: Hawaii, Mount Fujji

(d) Himalayas and Alps ranges

(e) Rift valley of East Africa

IX. Higher Order Thinking Skills (HOTs) Questions.

Question 1.
Consider the various sources of information related to the Earth’s Interior. Classify the above as DIRECT & INDIRECT sources of information. Give reasons.
Answer:
• Seismic activity
• Earth’s magnetism
• Volcanoes
• Mined rocks
• Gravitational force
• Meteors

• Seismic Activity: Frequency and size of earthquake.
• Earth’s magnetism: Due to the movement of molten material under the earth’s crust.
• Volcanoes: A rupture in the crust of a planetary mass object such as Earth, that allows hot lava, volcanic ash & gases to escape.
• Mined Rocks: Excavating hard minerals:
• Gravitational force: A natural phenomenon.
• Meteors: A bright streak of light.

Question 2.
Scientists use GPS to measure the rate of Tectonic Plate movements. Discuss.
Answer:
GPS works by sending radio signals from satellites to ground stations. The distance between the satellites and station is recorded. Over time, these distances change slightly. Scientists can measure the rate of Tectonic Plate movements by recording the time it takes for ground stations to move a given distance.

In-text HOTs Question

Question 1.
Pacific Ring of Fire — Most seismically and volcanically active. Why?
Answer:
The Pacific Ring of fire is an arc around the Pacific Ocean. It is associated with a nearly continuous series of oceanic trenches, volcanic arcs, and volcanic belts and plate movements. It has 452 volcanoes (more than 75% of the world’s active and dormant volcanoes). The Ring of Fire is a direct result of plate tectonics: the movement and collisions of lithospheric plates. That is why it is the most seismically and volcanically active zone in the world.

X. Life Skills

Imagine that you feel tremors or shocks in your locality. What will be your role in saving • lives from destruction? List out the Do’s and Don’ts.
Dos and don’ts during an earthquake
Do’s

1. Be aware that some earthquakes are actually foreshocks and a larger earthquake might occur.
2. If indoors, drop to the ground; cover your face and head with your arms and crouch in an inside comer of the building.
3. Stay away from glass, windows, outside doors and walls, and anything that could fall, (such as lighting fixtures or furniture).
4. Be aware that the electricity may go out or the sprinkler systems or fire alarms may turn on.
5. If outdoors, avoid moving. However, move away from buildings, trees, streetlights, and utility wires.
6. If you are in open space, stay there until the shaking stops.
7. If in a moving vehicle, stop as quickly as safety permits and stay in the vehicle. Avoid stopping near or under buildings, trees, overpasses, and utility wires.
8. If caught under debris, tap on a pipe or wall so rescuers can locate you. Shout if needed.

Don’ts

1. Do not light a match.
2. Do not move about or kick up dust.
3. Cover your mouth with a handkerchief or clothing.
4. Do not touch electrical switches.
5. Do not operate electrical appliances.

Student Activities

Question 1.
Collect a few rock samples from your area and classify them on the basis of what you have learnt.
Answer:
You can do this activity under the guidance of your teacher.

Question 2.
Narrate the processes involved in the given rock cycle diagram in your own words.
Answer:

Rocks are continually changing from one type to another and back again. Rock Cycle is the geologic process that describes the transition of rocks between the three rock types: igneous, sedimentary, and metamorphic. The forces inside the earth bring the rocks closer to the surface. Here the rocks are weathered, eroded and compacted. Then the forces on the earth sink the rocks. Back down, the rocks are heated, pressed and melted. So the elements that create rocks are constantly being recycled.

Question 3.
Here is a list of a few mountains.
• Ural Mountains, Andes Mountains, Vindhya Range, Alps mountains
• Satpura range, Rocky Mountains, Sierra Nevada.
• Identify and Locate with help of atlas
Answer:
You can identify and locate the above mentioned mountains with the help of an atlas or Internet.

Question 4.
(a) Arrange a few books one above the other on a table. Just shake the table and observe what happens.
Answer:
You can do this activity under the guidance of your teacher.

(b) Ask two students to hold two ends of a rope. Instruct one of them to shake the rope, while the other holds it lightly and then firmly. What do you observe?
Answer:
You can do this activity under the guidance of your teacher.

Question 5.
Take a bottle filled with soda. Give it a few shakes. Now twist the cap open. What do you observe?
Answer:
A capped bottle is under a uniform pressure. The molecules of carbon dioxide gas and liquid are at an equilibrium (due to a uniform pressure). When we shake the bottle, the contents are pressurized. So when the cap is opened, the liquid comes out with a force and fizz.

Lithosphere – I Endogenetic Processes Additional Questions

I. Choose the correct answer.

Question 1.
This is the solid outer part of the Earth.
(a) Lithosphere
(b) Atmosphere
(c) Hydrosphere
(d) Biosphere
Answer:
(a) Lithosphere

Question 2.
The presence of large quantities of …………… in the core is responsible for the Earth’s Gravitational force.
(a) Aluminium
(b) Magnesium
(c) Iron
(d) Silica
Answer:
(c) Iron

Question 3.
This is the store house of rocks.
(a) crust
(b) core
(c) mantle
(d) None of the above
Answer:
(a) crust

Question 4.
The word ‘Igneous’ is derived from the …………… word.
(a) Arabic
(b) Roman
(c) Latin
(d) Sanskrit
Answer:
(c) Latin

Question 5.
The movement of tectonic plates is due to …………… energy from the mantle.
(a) Atomic energy
(b) Hydro energy
(c) Wind energy
(d) Thermal energy
Answer:
(d) Thermal energy

Question 6.
These waves are the fastest of all the Earthquake waves.
(a) P – waves
(b) S – waves
(c) L- waves
(d) None of the above
Answer:
(a) P – waves

Question 7.
The sixth deadliest natural disaster due to Tsunami caused in the year …………..
(a) 1996
(b) 1998
(c) 2000
(d) 2004
Answer:
(d) 2004

Question 8.
…………… is a vent (or) and opening on the surface of the Earth crust.
(a) Volcano
(b) Tsunami
(c) Earthquake
(d) None of the above
Answer:
(a) Volcano

Question 9.
This is a dead volcano.
(a) Mt. St. Helens
(b) Mt. Kilimanjaro
(c) Mt. Fuji
(d) Paricutin
Answer:
(b) Mt. Kilimanjaro

Question 10.
Composite volcanoes are commonly found in the ………….. ocean.
(a) Pacific
(b) Southern
(c) Indian
(d) Atlantic
Answer:
(a) Pacific

II. Match the following.
(a)

Answer:
1. (b)
2. (c)
3. (a)
4. (e)
5. (d)

b.

Answer:
1. (d)
2. (a)
3. (b)
4. (c)

III. Consider the given statements

Question 1.
(i) When magnia reaches this Earth’s surface, it is referred to as ‘Lava’. (True)
(ii) The interior of the earth contains very hot molten material called ‘Magma’. (True)
(iii) Sedimentary are also called Primary (or) Mother rocks. (False)
(a) (i) is true
(b) (i) & (ii) are true (iii) false
(c) (iii) is true
(d) (i), (ii), (iii) are true
Answer:
(b) (i) and (ii) are true (iii) false

Question 2.
(i) The plates move vertically in convergent Boundary. (False)
(ii) The plates pull away from each other in Transform boundary. (False)
(iii) The plates slide horizontally past each other in Transform Boundary. (True)
(a) (i) is false
(b) (i) and (ii) are false
(c) (ii) false (i) and (iii) are true
(d) (i) (ii) are false (iii) true
Answer:
(i) (ii) are false (iii) true

IV. Answer the following questions in one or two sentences.

Question 1.
What is Hydrosphere?
Answer:
The Hydrosphere is the watery part of the Earth’s surface including oceans, rivers, lakes and water vapour.

Question 2.
What are fossils?
Answer:
The bodies of plants and animals that fall on the sedimentary rock deposits get embedded in the layers and form fossils.

Question 3.
What do you know about the Active Volcano?
Answer:
Active volcanoes are those which constantly eject volcanic lava, gases and fragmented materials, e g., Mount St. Helens in the United states.

Question 4.
What is Geology?
Answer:
The science that deals with the physical structure and substances of the earth their history and the processes which act on them.

Question 5.
What do the internal processes generate?
Answer:

• The internal processes generate heat and eject materials from deep below the Earth’s crust.
• Internal radio activity in the principal source of power for this process.

V. Give reasons for the following.

Question 1.
Why did Tsunami occur on 26th December 2004?
Answer:

• It was the result of the Indo-Australian plate subducting below the Eurasian plate.
• It was caused by an Earthquake measuring a magnitude of above 9 in the Richter scale.
  Hence the sea floor was uplifted, displacing the sea water above.

Question 2.
Why does the lava flow out in all directions in shield volcano?
Answer:

• Shield volcanoes are formed by intense viscous, lava.
• These are shallow depositions with gently sloping sides.
• Hence the lava flows out in all directions to create a shield.

VI. Distinguish between:

Question 1.
Internal Processes and External processes.
Answer:

Question 2.
Seismology and Geology.
Answer:

Question 3.
Atmosphere and Biosphere.
Answer:

VII. Write answers in a Paragraph.

Question 1.
Give an account of‘Tsunami’
Answer:
The word ‘Tsunami’ is a Japanese term, meaning harbour waves. It is adopted to describe large seismically generated sea waves caused by Earthquakes, submarine explosions and landslides. These waves travel at a great speed (more than 500 km per hour) and the length of the waves exceeds 600 km. These waves reach to a height of more than 15 m near the sea shore and are capable of causing destruction along the coastal area.

The 2004 Indian Ocean Earthquake that caused tsunami is the sixth-deadliest natural disaster which travelled at a speed of 600 km per hour with an estimated death toll of 2,80,000. The Earthquake which occurred near Indonesia at 00.58 hours took nearly 7 hours to reach Chennai.

You can Download Samacheer Kalvi 9th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 5 Coordinate Geometry Ex 5.2

9th Maths Coordinate Geometry Exercise 5.2 Question 1.
Find the distance between the following pairs of points.
(i) (1, 2) and (4, 3)
(ii) (3, 4) and (- 7, 2)
(ii) (a, b) and (c, b)
(iv) (3, -9) and (-2, 3)
Solution:
We know that distance,

9th Samacheer Maths Solution Ex 5.2 Question 2.
Determine whether the given set of points in each case are collinear or not.
(i) (7, -2), (5, 1), (3, 4)
(ii) (a, -2), (a, 3), (a, 0)
Solution:
(i) Let the points be A (7, -2), B (5, 1) and C (3, 4). By the distance formula.

∴ Hence the points are collinear.

(ii) Let the points be A (a, -2), B (a, 3) and C (a, 0).

∴ Hence the points are collinear.

Chapter 5 Coordinate Geometry Answers Question 3.
Show that the following points taken in order form an isosceles triangle.
(i) A (5, 4), B(2, 0), C (-2, 3)
(ii) A (6, -4),B (-2, -4), C (2, 10)
Solution:
(i) Let the points be A (5, 4), B (2, 0) and C (-2, 3)


Here AB + BC > CA and AB = BC. ∴ ∆ ABC is an isosceles triangle.

(ii) Let the points be A (6, -4), B (-2, -4) and C (2, 10).

Here BC + BA > CA and BC = CA. Two sides are equal, so ∆ ABC is an isosceles triangle

Coordinate Geometry Solutions Ex 5.2 Question 4.
Show that the following points taken in order form an equilateral triangle in each case.
(i) A(2, 2), B(-2, -2), C(\(-2 \sqrt{3}\), \(2 \sqrt{3}\))
(ii) A(\(\sqrt{3}\) ,2), B (0, 1), C(0, 3)
Solution:
(i) Let the points be A (2, 2) B (-2, -2) and C(\(-2 \sqrt{3}\), \(2 \sqrt{3}\))

All the 3 sides of ∆ABC are equal, Hence ∆ABC is an equilateral triangle.

(ii) Let the points be A (\(\sqrt{3}\), 2), B (0, 1) and C (0, 3).
All the 3 sides of ∆ABC are equal. Hence ∆ABC is an equilateral triangle.

Question 5.
Show that the following points taken in order form the vertices of a parallelogram.
(i) A(-3, 1), B(-6, -7), C (3, -9) and D(6, -1)
(ii) A (-7, -3), B(5, 10), C(15, 8) and D(3, -5)
Solution:
(i) Let A, B, C and D represent the points (-3, 1), (-6, -7) (3, -9) and (6, -1) respectively.

The opposite sides are equal. Hence ABCD is a parallelogram.

(ii) Let A, B, C and D represent the points (-7, -3), (5, 10) (15, 8) and (3, -5)

The opposite sides are equal. Hence ABCD is a parallelogram.

Form 3 Maths Exercise Question 6.
Verify that the following points taken in order form the vertices of a rhombus.
(i) A(3, -2), B (7, 6),C (-1, 2) and D (-5, -6)
(ii) A (1, 1), B(2, 1),C (2, 2) and D(1, 2)
Solution:
(i) Let the points be A(3, -2), B (7, 6), C (-1, 2) and D (-5, -6)

∴ All the four sides of quadrilateral ABCD are equal. Hence ABCD is a rhombus.

Question 7.
If A(-1, 1), B(1, 3) and C(3, a) are points and if AB = BC, then find ‘a’
Solution:

Maths Solutions For Class 9 Samacheer Kalvi Ex 5.2 Question 8.
The abscissa of a point A is equal to its ordinate, and its distance from the point B(1, 3) is 10 units, what are the coordinates of A?
Solution:


Co-ordinates of A are (-5, -5) or (9, 9)

9th Maths Book Ex 5.2 Question 9.
The point (x, y) is equidistant from the points (3, 4) and (-5, 6). Find a relation between x and y.
Solution:
P(x, y) is equidistant from the points A(3, 4) and B(-5, 6)

Geometry 5.2  9th Maths Ex 5.2 Question 10.
Let A(2, 3) and B(2, -4) be two points. If P lies on the x-axis, such that AP = \(\frac{3}{7}\)AB, find the coordinates of P.
Solution:

9th Maths Guide Ex 5.2 Question 11.
Show that the point (11, 2) is the centre of the circle passing through the points (1, 2), (3, -4) and (5, -6)
Solution:


Therefore S is the centre of the circle, passing through A, B and C.

5 Coordinate Geometry Ex 5.2 Question 12.
The radius of a circle with centre at origin is 30 units. Write the coordinates of the points where the circle intersects the axes. Find the distance between any two such points.
Solution:

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All these concepts of Chapter 1 Laws of Motion are explained very conceptually by the subject teachers in Tamilnadu State Board Solutions PDF as per the prescribed Syllabus & guidelines. You can download Samacheer Kalvi 10th Science Book Solutions Chapter 1 Laws of Motion State Board Pdf for free from the available links. Go ahead and get Tamilnadu State Board Class 10th Science Solutions of Chapter 1 Laws of Motion.

Tamilnadu Samacheer Kalvi 10th Science Solutions Chapter 1 Laws of Motion

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Samacheer Kalvi 10th Science Laws of Motion Textual Solved Problems

10th Science Laws Of Motion Book Back Answers Question 1.
Calculate the velocity of a moving body of mass 5 kg whose linear momentum is 2.5 kg ms^-1.
Solution:
Linear momentum = mass × velocity
Velocity = \(\frac { linear momentum }{ mass }\)
V = \(\frac { 2.5 }{ 0.5 }\) = 0.5 ms^-1.

Laws Of Motion Class 10 Questions And Answers Question 2.
A door is pushed, at a point, whose distance from the hinges is 90 cm, with a force of 40 N. Calculate the moment of the force about the hinges.
Solution:
Formula: The moment of a force M = F × d
Given: F = 40 N and d = 90 cm = 0.9 m.
Hence, moment of the force = 40 × 0.9 = 36 Nm.

Laws Of Motion Class 10 Samacheer Question 3.
At what height from the centre of the Earth the acceleration due to gravity will be \(\frac { 1 }{ 4 }\)th of its value as at the Earth.
Solution:
Data: Height from the centre of the Earth, R’ = R + h
The acceleration due to gravity at that height, g’ = \(\frac { g }{ 4 }\)
Formula:

From the centre of the Earth, the object is placed at twice the radius of the earth.

Samacheer Kalvi 10th Science Laws of Motion Textbook Evaluation

I. Choose the correct answer.

Laws Of Motion Class 10 Book Back Answers 1.
The inertia of a body depends on _____ .
(a) weight of the object
(b) acceleration due to gravity of the planet
(c) mass of the object
(d) Both a & b.
Answer:
(c) mass of the object

10th Science Unit 1 Question 2.
Impulse is equals to:
(a) rate of change of momentum
(b) rate of force and time
(c) change of momentum
(d) rate of change of mass
Answer:
(c) change of momentum

10th Science Laws Of Motion Question 3.
Newton’s III law is applicable to ______ .
(a) for a body is at rest
(b) for a body in motion
(c) both a & b
(d) only for bodies with equal masses.
Answer:
(c) both a & b

10th Law Of Motion Question 4.
Plotting a graph for momentum on the X-axis and time on Y-axis. The slope of the momentum-time graph gives:
(a) Impulsive force
(b) Acceleration
(c) Force
(d) Rate of force
Answer:
(c) Force

Laws Of Motion – Class 10 New Syllabus Question 5.
In which of the following sport the turning of the effect of force used?
(a) swimming
(b) tennis
(c) cycling
(d) hockey.
Answer:
(c) cycling

10th Physics Laws Of Motion Question 6.
The unit of ‘g’ is ms^-2. It can be also expressed as _____ .
(a) cm s^-1
(b) N kg^-1
(c) Nm² kg^-1
(d) cm² s^-2
Answer:
(b) N kg^-1

Laws Of Motion 10th Science Question 7.
One kilogram force equals to:
(a) 9.8 dyne
(b) 9.8 × 10⁴ N
(c) 98 × 10⁴ dyne
(d) 980 dyne
Answer:
(c) 98 × 10⁴ dyne

10th Standard Science Laws Of Motion Question 8.
The mass of a body is measured on planet Earth as M kg. When it is taken to a planet of radius half that of the Earth then its value will be ____ kg.
(a) 4M
(b) 2M
(c) \(\frac { M }{ 4 }\)
(d) M.
Answer:
(c) \(\frac { M }{ 4 }\)

10th Science Law Of Motion Question 9.
If the Earth shrinks to 50% of its real radius its mass remaining the same, the weight of a body on the Earth will _____ .
(a) decrease by 50%
(b) increase by 50%
(c) decrease by 25%
(d) increase by 300%.
Answer:
(c) decrease by 25%

Laws Of Motion Class 10 In Tamil Question 10.
To project the rockets which of the following
principle(s) is /(are) required?
(a) Newton’s third law of motion
(b) Newton’s law of gravitation
(c) Law of conservation of linear momentum
(d) Both (a) and (c)
Answer:
(d) Both (a) and (c)

II. Fill in the blanks.

10th Science Lesson 1 Question 1.
To produce a displacement _____ is required.
Answer:
force.

10th Science Solution Samacheer Kalvi Question 2.
Passengers lean forward when the sudden brake is applied in a moving vehicle. This can be explained by ____.
Answer:
the inertia of motion.

Samacheer Kalvi Guru 10th Science Question 3.
By convention, the clockwise moments are taken as _____ and the anticlockwise moments are taken as _____.
Answer:
negative, positive.

10th Science Solutions Samacheer Kalvi Question 4.
______ is used to change the speed of the car.
Answer:
Acceleration.

10th Science Solutions Samacheer Question 5.
A man of mass 100 kg has a weight of _____ at the surface of the Earth.
Answer:
980 N.

III. State whether the following statements are true or false. Correct the statement if it is false:

Class 10 Samacheer Kalvi Science Solutions Question 1.
The linear momentum of a system of particles is always conserved.
Answer:
False.
Correct Statement: The linear momentum of a system of particles is always conserved if no external force acts.

10th Samacheer Kalvi Science Solutions Question 2.
The apparent weight of a person is always equal to his actual weight.
Answer:
True.

Question 3.
Weight of a body is greater at the equator and less at the polar region.
Answer:
False.
Correct Statement: Weight of a body is lesser at the equator and greater at the polar region.

Question 4.
Turning a nut with a spanner having a short handle is so easy than one with a long handle.
Answer:
False.
Correct Statement: Turning a nut with a spanner having a short handle is so harder than one with a long handle.

Question 5.
There is no gravity in the orbiting space station around the Earth. So the astronauts feel weightlessness.
Answer:
False.
Correct Statement: There is a gravity in the orbiting space station around the earth. Since space station and astronauts have equal acceleration. Both the astronauts and space station are in the state of weightlessness.

IV. Match the following.

Question 1.

Answer:
1. (b) Stable equilibrium of a body
2. (c) Law of force
3. (d) Flying nature of a bird
4. (a) Propulsion of a rocket

V. Assertion & Reasoning

Mark the correct choice as
(a) If both the assertion and the reason are true and the reason is the correct explanation of assertion.
(b) If both the assertion and the reason are true, but the reason is not the correct explanation of the assertion.
(c) Assertion is true, but the reason is false.
(d) Assertion is false, but the reason is true.

Question 1.
Assertion: The sum of the clockwise moments is equal to the sum of the anticlockwise moments.
Reason: The principle of conservation of momentum is valid if the external force on the system is zero.
Answer:
(b) If both the assertion and the reason are true, but the reason is not the correct explanation of the assertion.

Question 2.

1. Assertion: The value of ‘g’ decreases as height and depth increase from the surface of the Earth.
2. Reason: ‘g’ depends on the mass of the object and the Earth.

Answer:
(c) The assertion is true, but the reason is false.

VI. Answer briefly.

Question 1.
Define inertia. Give its classification.
Answer:
Inertia: The inherent property of a body to resist any change in its state of rest or the state of uniform motion, unless it is influenced upon by an external unbalanced force, is known as ‘inertia’.
Types of Inertia

• Inertia of rest
• Inertia of motion
• Inertia of direction

Question 2.
Classify the types of force based on their application.
Answer:

1. Like parallel forces
2. Unlike parallel forces

Question 3.
If a 5 N and a 15 N forces are acting opposite to one another. Find the resultant force and the direction of action of the resultant force.
Solution:
The two forces are unlike parallel forces

Let P = 5N, Q = 15N
Resultant force (R) = P – Q = 5 + (-15) = -10N
R = -10N.
The resultant force acting along the direction of “Q”.

Question 4.
Differentiate mass and weight.
Answer:

Question 5.
Define moment of a couple.
Answer:
Rotating effect of a couple is known as moment of a couple.
Moment of a couple = Force × perpendicular distance between the line of action of forces
M = F × S

Question 6.
State the principle of moments.
Answer:
When a number of like or unlike parallel forces act on a rigid body and the body is in equilibrium, then the algebraic sum of the moments in the clockwise direction is equal to the algebraic sum of the moments in the anticlockwise direction.

Question 7.
State Newton’s second law.
Answer:
“The force acting on a body is directly proportional to the rate of change of linear momentum of the body and the change in momentum takes place in the direction of the force”.

Question 8.
Why a spanner with a long handle is preferred to tighten screws in heavy vehicles?
Answer:
This is because turning effect to tighten the screws depends upon the perpendicular distance of the applied force from the axis of rotation is power arm. Larger the power armless is the force required to turn the screws. So spanner is provided with a long handle.

Question 9.
While catching a cricket ball the fielder lowers his hands backwards. Why?
Answer:
(i) When the fielder lowers his hands backwards, he increases the value of time of collision and so retardation is decreased.
(ii) Hence retarding force becomes lesser than before and the palm of the fielder is not hurt very much.

Question 10.
How does an astronaut float in a space shuttle?
Answer:
An astronaut float in a space shuttle because both are in the state of weightlessness. Both are experiencing equal acceleration towards earth as free fall bodies. Astronauts are not floating but falling freely.

VII. Solve the given problems.

Question 1.
Two bodies have a mass ratio of 3 : 4. The force applied to the bigger mass produces an acceleration of 12 ms^-2. What could be the acceleration of the other body, if the same force acts on it?
Solution:
Mass ratio of the bodies = 3 : 4 and same force is (m₁ : m₂) acting on the body and a₂ = 12 ms^-2
∴ m₁a₁ = m₂a₂
\(\frac{m_{1}}{m_{2}}=\frac{a_{2}}{a_{1}} \Rightarrow \frac{3}{4}=\frac{a_{2}}{a_{1}}\)
\(a_{1}=\frac{4}{3} \times 12=16 \mathrm{ms}^{-2}\)

Question 2.
A ball of mass 1 kg moving with a speed of 10 ms^-1 rebounds after a perfectly elastic collision with the floor. Calculate the change in linear momentum of the ball.
Solution:
Mass of a ball = 1 kg
Velocity of the bail before collision,
u = 10 m/s
Velocity of the ball after collision,
v = – u
= -10 m/s
Change in momentum,
P = m(v – u)
P = 1(-10 – 10)
= -20 kg m/s.

Question 3.
A mechanic unscrews a nut by applying a force of 140 N with a spanner of length 40 cm. What should be the length of the spanner if a force of 40 N is applied to unscrew the same nut?
Solution:
Given F₁ = 140 N, d₁ = 40 cm, F₂ = 40 N, d₂ = ?
In, both the cases, moment of forces applied are equal
F₁d₁ = F₂d₂
\(\begin{array}{l}{d_{2}=\left(\frac{F_{1}}{F_{2}}\right) d_{1}} \\ {d_{2}=40 \times \frac{140}{40}=140 \mathrm{cm}}\end{array}\)

Question 4.
The ratio of masses of two planets is 2 : 3 and the ratio of their radii are 4 : 7 Find the ratio of their accelerations due to gravity.
Solution:
The ratio of masses of two planets m₁ : m₂ = 2 : 3
The ratio of radii of two planets R₁ : R₂ = 4 : 7
Formula:

VIII. Answer in detail.

Question 1.
What are the types of inertia? Give an example for each type.
Answer:
Types of Inertia:
(i) Inertia of rest: The resistance of a body to change its state of rest is called inertia of rest. Eg: When you vigorously shake the branches of a tree, some of the leaves and fruits are detached and they fall down.

(ii) Inertia of motion: The resistance of a body to change its state of motion is called inertia of motion. Eg: An athlete runs some distance before jumping. Because, this will help him jump longer and higher.

(iii) Inertia of direction: The resistance of a body to change its direction of motion is called inertia of direction. Eg: When you make a sharp turn while driving a car, you tend to lean sideways.

Question 2.
State Newton’s laws of motion.
Answer:
Newton’s First Law: Everybody continues to be in its state of rest or the state of uniform motion along a straight line unless it is acted upon by some external force.

Newtons Second law: The force acting on a body is directly proportional to the rate of change of linear momentum of the body and the change in momentum takes place in the direction of the force.

Newtons Third Law: For every action, there is an equal and opposite reaction. They always act on two different bodies.

Question 3.
Deduce the equation of a force using Newton’s second law of motion.
Answer:
“The force acting on a body is directly proportional to the rate of change of linear momentum of the body and the change in momentum takes place in the direction of the force”.
Let, ‘m’ be the mass of a moving body, moving along a straight line with an initial speed ‘u’ After a time interval of ‘t’, the velocity of the body changes to ‘v’ due to the impact of an unbalanced external force F.
Initial momentum of the body (P_i) = mu
Final momentum of the body (P_f) = mv
Change in momentum ∆p = P_f – P_i = mv – mu
By Newton’s second law of motion,
Force, F ∝ rate of change of momentum
F ∝ change in momentum / time
\(\begin{array}{l}{\mathrm{F} \propto \frac{m v-m u}{t}} \\ {\mathrm{F}=\frac{k m(v-u)}{t}}\end{array}\)
Here, k is the proportionality constant, k = 1 in all systems of units.
Hence, \(\mathrm{F}=\frac{m(v-u)}{t}\)
Since, acceleration = change in velocity / time,
a = (v – u)/t.
Hence, we have F = m × a
Force = mass × acceleration

• No external force is required to maintain the motion of a body moving with uniform velocity.
• When the net force acting on a body is not equal to zero, then definitely the velocity of the body will change.
• Thus, change in momentum takes place in the direction of the force. The change may take place either in magnitude or in direction or in both.

Question 4.
State and prove the law of conservation of linear momentum.
Answer:
(i) There is no change in the linear momentum of a system of bodies as long as no net external force acts on them.
(ii) Let us prove the law of conservation of linear momentum with the following illustration:

(iii) Let two bodies A and B having masses m1 and m2 move with initial velocity u₁ and u₂ in a straight line.
(iv) Let the velocity of the first body be higher than that of the second body. i.e., u₁ > u₂.
(v) During an interval of time t second, they tend to have a collision. After the impact, both of them move along the same straight line with a velocity v₁ and v₂ respectively.
Force on body B due to A,
\(\mathrm{F}_{\mathrm{B}}=\frac{m_{2}\left[v_{2}-u_{2}\right]}{t}\)
Force on body A due to B,
\(\mathrm{F}_{\mathrm{A}}=\frac{m_{1}\left[v_{1}-u_{1}\right]}{t}\)
By Newton’s III law of motion, Action force = Reaction force
F_A = -F_B
\(\begin{aligned} \frac{m_{1}\left[v_{1}-u_{1}\right]}{t} &=\frac{m_{2}\left[v_{2}-u_{2}\right]}{t} \\ m_{1} v_{1}+m_{2} v_{2} &=m_{1} u_{1}+m_{2} u_{2} \end{aligned}\)
The above equation confirms in the absence of an external force, the algebraic sum of the momentum after collision is numerically equal to the algebraic sum of the momentum before collision.
Hence the law of conservation linear momentum is proved.

Question 5.
Describe rocket propulsion.
Answer:
Propulsion of rockets is based on the law of conservation of linear momentum as well as Newton’s III law of motion. Rockets are filled with a fuel (either liquid or solid) in the propellant tank. When the rocket is fired, this fuel is burnt and a hot gas is ejected with a high speed from the nozzle of the rocket, producing a huge momentum. To balance this momentum, an equal and opposite reaction force is produced in the combustion chamber, which makes the rocket project forward.

While in motion, the mass of the rocket gradually decreases, until the fuel is completely burnt out. Since, there is no net external force acting on it, the linear momentum of the system is conserved. The mass of the rocket decreases with altitude, which results in the gradual increase in velocity of the rocket. At one stage, it reaches a velocity, which is sufficient to just escape from the gravitational pull of the Earth. This velocity is called escape velocity.

Question 6.
State the universal law of gravitation and derive its mathematical expression.
Answer:
This law states that every particle of matter in this universe attracts every other particle with a force. This force is directly proportional to the product of their masses and inversely proportional to the square of the distance between the centres of these masses. The direction of the force acts along the line joining the masses.

The force between the masses is always attractive and it does not depend on the medium where they are placed.
Let, m₁ and m₂ be the masses of two bodies A and B placed r metre apart in space.
Force F ∝ m₁ × m₂
F ∝ \(1 / r^{2}\)
On combining the above two expressions
\(\begin{array}{l}{\mathrm{F} \propto \frac{m_{1} \times m_{2}}{r^{2}}} \\ {\mathrm{F}=\frac{\mathrm{G} m_{1} m_{2}}{r^{2}}}\end{array}\)
Where G is the universal gravitational constant.
Its value in SI unit is 6.674 × 10^-11 Nm² kg^-2.

Question 7.
Give the applications of the universal law of gravitation.
Answer:
Application of Newton’s law of gravitation are:
(i) Dimensions of the heavenly bodies can be measured using the gravitation law. Mass of the Earth, radius of the Earth, acceleration due to gravity, etc., can be calculated with a higher accuracy.
(ii) Helps in discovering new stars and planets.
(Hi) Helps to explain germination of roots is due to the property of geotropism which is the property of a root responding to the gravity.
(iv) One of the irregularities in the motion of stars is called ‘Wobble’ lead to the disturbance in the motion of a planet nearby. In this condition the mass of the star can be calculated using the law of gravitation.
(v) Helps to predict the path of the astronomical bodies.

IX. HOT Questions.

Question 1.
Two blocks of masses 8 kg and 2 kg respectively, lie on a smooth horizontal surface in contact with one other. They are pushed by a horizontally applied force of 15 N. Calculate the force exerted on the 2 kg mass.
Solution:

Given: m₁ = 8 kg, m₂ = 2 kg, F = 15 N
F = mtotal, F = (m₁ + m₂) a = (8 + 2) a = 10 a
15 = 10 a
⇒ a = \(\frac{15}{10}=\frac{3}{2}\) ms^-2
Force exerted by mass of 8 kg
F = m₁ a = \(8 \times \frac{3}{2}\) = 12 N.

Question 2.
A heavy truck and bike are moving with the same kinetic energy. If the mass of the truck is four times that of the bike, then calculate the ratio of their momenta. (Ratio of momenta = 1 : 2)
Solution:
Given: Let m₁, m₂ are the masses of truck and bike.
m₁ = 4m₂
Here kinetic energies of both truck and bike are same
\(\begin{aligned} m_{1} v_{1}^{2} &=m_{2} v_{2}^{2} \\ 4 m_{2} v_{1}^{2} &=m_{2} v_{2}^{2} \\ \frac{v_{1}}{v_{2}} &=\frac{1}{2} \\ v_{2} &=2 v_{1} \end{aligned}\)
Ratio of momenta: \(\frac{p_{1}}{p_{2}}=\frac{m_{1} v_{1}}{m_{2} v_{2}}=\frac{4 m_{2}}{m_{2}} \cdot \frac{v_{1}}{2 v_{1}}\) = 2
P₁ : P₂ = 2 : 1.

Question 3.
“Wearing a helmet and fastening the seat belt is highly recommended for the safe journey”.Justify your answer using Newton’s laws of motion.
Answer:
During the motion of car and two wheelers, when the brakes are applied, the vehicles slow down but our body tends to continue in the same state of motion due to inertia. So this may cause injury to passengers. Hence they are advised to wear a helmet and seat belt.

Samacheer Kalvi 10th Science Laws of Motion Additional Questions

I. Choose the correct answer.

Question 1.
A cricketer catches a ball of mass 150 gm in 0.1s and which is moving with a speed of 20 ms^-1, then he experiences the force of ____ _.
(a) 300 N
(b) 30 N
(c) 3 N
(d) 0.3 N.
Answer:
(b) 30 N
Hint: Impulse = change in momentum
F.∆t = mv – mu
\(\mathrm{F}=\frac{m v-m u}{\Delta t}\)
\(=\frac{150 \times 10^{-3} \times 20}{0.1}=30 \mathrm{N}\)

Question 2.
SI unit of force is:
(a) Dyne
(b) newton
(c) kgms^-1
(d) Joule
Answer:
(b) newton

Question 3.
A coin is dropped in a lift. It takes time t₁ to reach the floor, when the lift is stationary, it takes time t₂, when the lift is moving up with constant acceleration, then ____ _.
(a) t₁ > t₂
(b) t₁ < t₂
(c) t₁ = t₂
(d) None.
Answer:
(a) t₁ > t₂

Question 4.
An unbalanced force acts on a body, the body:
(a) must remain at rest
(b) must be accelerated
(c) must move with uniform velocity
(d) move with uniform motion
Answer:
(b) must be accelerated

Question 5.
A satellite in its orbit around the earth is weightless on account of its _____.
(a) velocity
(b) momentum
(c) angular momentum
(d) acceleration.
Answer:
(c) angular momentum

Question 6.
When two or more forces acting on a body and the body does not change its position, then the forces are:
(a) imbalanced
(b) mechanical force
(c) balanced forces
(d) none
Answer:
(c) balanced forces

Question 7.
What would be the acceleration due to gravity at another planet, whose mass and radius core twice that of earth?
(a) g
(b) \(\frac{g}{2}\)
(c) \(\frac{g}{4}\)
Answer:
(b) \(\frac{g}{2}\)
Hint: We know that \(\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^{2}}\)
\(\frac{g_{1}}{g_{2}}=\frac{\left(\frac{\mathrm{GM}}{\mathrm{R}^{2}}\right)}{\left(\frac{\mathrm{G} .2 \mathrm{M}}{4 \mathrm{R}^{2}}\right)}\)
\(\frac{g_{1}}{g_{2}}=2 \quad \Rightarrow \quad g_{2}=\frac{1}{2} g_{1}\)

Question 8.
At sea level, the value of “g” is maximum at _____.
(a) the poles
(b) the equator
(c) 45° south latitude
(d) 45° north of longitude.
Answer:
(a) the poles

Question 9.
An object cannot change the state of rest or motion, until a force is applied. This inability of the object is called:
(a) inertia
(b) mass
(c) weight
(d) acceleration
Answer:
(a) inertia

Question 10.
The ability of a body to maintain its state of rest or motion is called ______.
(a) mechanics
(b) kinematics
(c) kinetics
(d) Inertia.
Answer:
(d) Inertia.

Question 11.
_____ deals with the bodies, which are at rest under the action of forces.
(a) Statics
(b) Dynamics
(c) Kinematics
(d) Kinetics.
Answer:
(a) Statics

Question 12.
A motor car starts from rest and moves after 5 seconds. If its velocity is 200 m/s then its acceleration is:
(a) 100 m/s²
(b) 40 m/s²
(c) 20 m/s²
(d) 80 m/s²
Answer:
(b) 40 m/s²

Question 13.
_____ deals with the motion of bodies considering the cause of motion.
(a) Force
(b) Dynamics
(c) Statics
(d) Kinetics.
Answer:
(d) Kinetics

Question 14.
Linear momentum = _____
(a) mass × velocity
(b) mass × distance
(c) distance × time
(d) \(\frac{\text { mass }}{\text { velocity }}\).
Answer:
(a) mass × velocity

Question 15.
The inability of the body to change its state is:
(a) force
(b) momentum
(c) acceleration
(d) inertia
Answer:
(d) inertia

Question 16.
Two or more forces of equal or unequal magnitude acting along the same direction, parallel to each other are called _____.
(a) like parallel forces
(b) unlike parallel forces
(c) resultant force
(d) balanced force.
Answer:
(a) like parallel forces

Question 17.
The axis of the fixed edge about which the thing is rotated is called as _____ .
(a) axis of rotation
(b) fixed axis rotation
(c) point of rotation
(d) Fixed point.
Answer:
(a) axis of rotation

Question 18.
When a net force acts on an object, the object will be accelerated in the direction of force with an acceleration proportional to:
(a) force on the object
(b) velocity
(c) mass
(d) inertia
Answer:
(a) force on the object

Question 19.
Rotating effect of a couple is known as ______ .
(a) product of forces
(b) the momentum of a couple
(c) mass
(d) momentum.
Answer:
(b) momentum of a couple

Question 20.
The amount of force required to produce an acceleration of 1 ms^-2 in a body of mass _____ is called unit force.
(a) 10 kg
(b) 100 kg
(c) 1 kg
(d) 0 kg.
Answer:
(c) 1 kg

Question 21.
The acceleration of a body is due to:
(a) balance force
(b) electrostatic force
(c) unbalanced force
(d) conservative force
Answer:
(c) unbalanced force

Question 22.
Universal gravitational constant ______ .
(a) G = 6.684 × 10^-10 Nm² kg^-1
(b) G = 7.4 × 10¹⁰ Nm²
(c) G = 6.623 × 10¹¹ Nm² kg^-1
(d) G = 6.674 × 10^-11 Nm² kg^-2
Answer:
(d) G = 6.674 × 10^-11 Nm² kg^-2

Question 23.
Mean value of the acceleration due to gravity is ______ .
(a) 10.1 ms^-2
(b) 8.8 ms^-2
(c) 9.8 ms^-2
(d) 9.8 ms.
Answer:
(c) 9.8 ms^-2

Question 24.
The unit of weight is:
(a) kg
(b) g
(c) Newton
(d) ms^-1
Answer:
(c) Newton

Question 25.
The value of accelaration due to gravity on the surface of the moon is _____ .
(a) 1.75 ms^-1
(b) 3.8 ms^-2
(c) 1.625 ms^-2
(d) 1.625 ms^-1
Answer:
(c) 1.625 ms^-2

Question 26.
The unit of weight is _____ .
(a) kg m
(b) kg
(c) newton
(d) kg m^-1
Answer:
(c) newton

Question 27.
The weight of a body is _____ poles than at the equatorial region.
(a) more
(b) less
(c) zero
(d) one.
Answer:
(a) more

Question 28.
In a collision between a heavier body and a lighter body, which body experiences greater force?
(a) heavier body
(b) lighter body
(c) both the body experience same force
(d) both body exchange acceleration
Answer:
(c) both the body experience same force

II. Fill in the blanks.

Question 1.
Turning a tap is an example of ____
Answer:
couple.

Question 2.
Torque is a _______ quantity.
Answer:
vector.

Question 3.
1 gf is equal to _____ dyne.
Answer:
980.

Question 4.
The resultant force acting on a body is equal to zero then the body will be in ______
Answer:
equilibrium.

Question 5.
The force equal to resultant but opposite in direction is ______
Answer:
equilibrate.

Question 6.
The product of force and time is ______
Answer:
impulse.

Question 7.
The force between the masses is always ______
Answer:
attractive.

Question 8.
The quantity of matter contained in the object is known as _____
Answer:
mass.

Question 9.
The magnitude of the universal gravitational constant is _____.
Answer:
6.674 × 10^-11 Nm² kg^-2

Question 10.
Propulsion of rockets is based on the ____ and ____
Answer:
Law of conservation of linear momentum & Newton’s third law.

Question 11.
Parallel unequal forces are acting in ______ directions.
Answer:
Opposite.

Question 12.
Torque and force are the ____ quantities.
Answer:
vector.

Question 13.
The unit of moment of a couple is _____ .
Answer:
newton metre (Nm).

Question 14.
A _____ enables you to manoeuvre a car easily by transferring a _______ to the wheels with less effort.
Answer:
steering wheel, torque.

Question 15.
_____ is required to produce the acceleration of a body.
Answer:
Force.

Question 16.
The acceleration is produced along the radius is called ______
Answer:
centripetal acceleration.

Question 17.
______ is equal to the magnitude of change in momentum.
Answer:
impulse.

Question 18.
A large force acting for a very short interval of time is called as ______ .
Answer:
impulse Force.

Question 19.
Mass of the earth _____
Answer:
5.972 × 10²⁴ kg.

Question 20.
The relation between acceleration due to gravity (g) and the universal gravitational constant (G) is _____ .
Answer:
\(g=\frac{G M}{R^{2}}\).

III. State whether the following statements are true or false, correct the statement if it is false.

Question 1.
Rest and motion are interrelated terms.
Answer:
True.

Question 2.
In the C.G.S. system, the unit of linear momentum is kg ms^-1.
Answer:
False.
Correct Statement: In the C.G.S. system, the unit of linear momentum is g cms^-1.

Question 3.
An external force is required to maintain the motion of a body moving with uniform velocity.
Answer:
False.
Correct Statement: No external force is required to maintain the motion of a body moving with uniform velocity.

Question 4.
The amount of force required for a body of mass 1 gram produces an acceleration of 1 cm s^-2
Answer:
True.

Question 5.
By Newton’s III – law of motion, the action force is not equal to the reaction force.
Answer:
False.
Correct Statement: By Newton’s III – law of motion, the action force is equal to the reaction force.

Question 6.
The value of acceleration due to gravity (g) is not the same at all the points on the surface of the earth.
Answer:
True.

Question 7.
The value of acceleration due to gravity on the surface of the moon is 1.625 ms^-2.
Answer:
True.

Question 8.
The regularities in the motion of stars are called ‘wobble’.
Answer:
False.
Correct Statement: The irregularities in the motion of stars is called ‘wobble’.

Question 9.
Mechanics is divided into kinematics and kinetics.
Answer:
False.
Correct Statement: Mechanics is divided into statics and dynamics.

Question 10.
Application of Newton’s law of gravitation helps to predict the path of the astronomical bodies.
Answer:
True.

IV. Match the following.

Question 1.

Answer:
1. (d) Mass and velocity
2. (a) Mass and acceleration
3. (e) Force and perpendicular distance
4. (b) Change in momentum
5. (c) GM/R²

Question 2.

Answer:
1. (d) The Motion of bodies with cause
2. (c) The Motion of bodies without cause
3. (b) In equilibrium
4. (a) Causes the motion

V. Assertion & Reasoning

Mark the correct choice as
(a) If both the assertion and the reason are true and the reason is the correct explanation of assertion.
(b) If both the assertion and the reason are true, but the reason is not the correct explanation of the assertion.
(c) Assertion is true, but the reason is false.
(d) Assertion is false, but the reason is true.

Question 1.
Assertion: At poles value of acceleration due to gravity (g) is greater than that of the equator.
Reason: Earth rotates on its axis in addition to revolving around the sun.
Answer:
(a) If both the assertion and the reason are true and the reason is the correct explanation of assertion.

Question 2.
Assertion: The force exerted by the earth on an apple is more than that exerted by apple on the earth.
Reason: The force on apple exerts on the earth is determined by the mass of the apple only.
Answer:
(d) The assertion is false but the reason is true

Question 3.
Assertion: A freely falling body is in the state of weightlessness
Reason: A body becomes conscious of its weight only when it is opposed
Answer:
(a) If both the assertion and the reason are true and the reason is the correct explanation of assertion.

Question 4.
Assertion: Newton’s third law of motion is applicable only when bodies are in motion.
Reason: Newton’s third law applies to all types of forces, e.g. gravitational, electric or magnetic forces.
Answer:
(d) The assertion is false but the reason is true.

Question 5.
Assertion: The apparent weight of the person is zero, in which condition or state is known as weightless.
Reason: When the person in a lift moves down with an acceleration (a) is equal to the acceleration due to gravity (g)
Answer:
(a) If both the assertion and the reason are true and the reason is the correct explanation of assertion.

Question 6.
Assertion: A gear is a circular wheel with teeth around its rim.
Reason: It helps to change the speed of rotation of a wheel by changing the force and helps to transmit power.
Answer:
(c) The assertion is true, but the reason is false.

Question 7.
Assertion: Mass of a body is defined as the gravitational force exerted on it due to earth’s gravity alone
Reason: Weight = mass × acceleration due to gravity.
Answer:
(d) The assertion is false, but the reason is true.

Question 8.
Assertion: Weight is a vector quantity.
Reason: Direction of weight is always towards the centre of the earth.
Answer:
(a) If both the assertion and the reason are true and the reason is the correct explanation of assertion.

Question 9.
Assertion: Resultant force is equal to the vector sum of all the forces.
Reason: A system cannot be brought to equilibrium by applying another force.
Answer:
(b) If both the assertion and the reason are true, but the reason is not the correct explanation of the assertion.

VI. Answer briefly

Question 1.
Define Linear momentum.
Answer:
The product of mass and velocity of a moving body gives the magnitude of linear momentum. It acts in the direction of the velocity of the object. Linear momentum is a vector quantity.
Linear Momentum = mass × velocity.
Unit of momentum in SI system is Kg ms^-1 and in C.G.S system its unit is g cm s^-1

Question 2.
What is the resultant force?
Answer:
When several forces act simultaneously on the same body, then the combined effect of the multiple forces can be represented by a single force, which is termed as ‘resultant force’.

Question 3.
What is meant by equilibrant?
Answer:
A system can be brought to equilibrium by applying another force, which is equal to the resultant force in magnitude, but opposite in direction. Such force is called as ‘Equilibrant’.

Question 4.
Explain the Newton third law of motion with examples.
Answer:
‘For every action, there is an equal and opposite reaction. They always act in two different bodies’.
Example: When you fire a bullet, the gun recoils backwards and the bullet is moving forward (Action) and the gun equalises this forward action by moving backwards (Reaction).

Question 5.
How did the change in momentum achieve?
Answer:
Change in momentum can be achieved in two ways. They are:

• A large force acting for a short period of time and
• A smaller force acting for a longer period of time.

Question 6.
Define impulse.
Answer:
A large force acting for a very short interval of time is called as ‘Impulsive force’.When a force F acts on a body for a period of time t, then the product of force and time is known as ‘impulse’ represented by ‘J’
Impulse, J = F × t …….. (1)
By Newton’s second law
F = ∆p / t (A refers to change)
∆p = F × t ………. (2)
From (1) and (2)
J = ∆p
Impulse is also equal to the magnitude of change in momentum.
Its unit is kg ms^-1 or Ns.

Question 7.
What is meant by free fall?
Answer:

1. When the person in a lift moves down with an acceleration (a) equal to the acceleration due to gravity (g), i.e., when a = g, this motion is called as ‘free fall’.
2. The apparent weight (R = m (g – g) = 0) of the person is zero. This condition or state refers to the state of weightlessness.

Question 8.
Define weightlessness.
Answer:
Whenever a body or a person falls freely under the action of Earth’s gravitational force alone, it appears to have zero weight. This state is referred to as ‘weightlessness’.

Question 9.
Explain the various causes of the apparent weight of a person in a moving lift.
Answer:

Question 10.
Explain the variation of acceleration due to gravity.
Answer:
Variation of acceleration due to gravity (g):

1. Since, g depends on the geometric radius of the Earth, (g ∝ 1 / R²), its value changes from one place to another on the surface of the Earth.
2. The geometric radius of the Earth is maximum in the equatorial region and minimum in the polar region, the value of g is maximum in the polar region and minimum at the equatorial region.
3. When you move to a higher altitude from the surface of the Earth, the value of g reduces.
4. when you move deep below the surface of the Earth, the value of g reduces. Value of g is zero at the centre of the Earth.

Question 11.
Define one newton and one dyne.
Answer:
Definition of 1 newton (N): The amount of force required for a body of mass 1 kg produces an acceleration of 1 ms^-2, 1 N = 1 kg ms^-2
Definition of 1 dyne: The amount of force required for a body of mass 1 gram produces an acceleration of 1 cms^-2, 1 dyne = 1 g cms^-2; also 1 N = 10⁵ dyne.

Question 12.
How can you measure the moment of the couple?
Answer:
(i) Rotating effect of a couple is known as the moment of a couple.
(ii) Moment of a couple is measured by the product of any one of the forces and the perpendicular distance between the line of action of two forces. The turning effect of a couple is measured by the magnitude of its moment.
(iii) Moment of a couple = Force × perpendicular distance between the line of action of forces
M = F × S
(iv) The unit of moment of a couple is newton metre (N m) in SI system and dyne cm in the CGS system.
(v) By convention, the direction of moment of a force or couple is taken as positive if the body is rotated in the anti-clockwise direction and negative if it is rotating in the clockwise direction.
They are shown in Figures.

Question 13.
Define Torque.
Answer:
(i) The rotating or turning effect of a force about a fixed point or fixed axis is called the moment of the force about that point or torque (τ).
(ii) τ = F × d
(iii) Torque is a vector quantity.
(iv) Its SI unit is Nm.

VII. Answ er in detail.

Question 1.
Explain any three application of Torque.
Answer:
Application of Torque:
(i) Gears: A gear is a circular wheel with teeth around its rim. It helps to change the speed of rotation of a wheel by changing the torque and helps to transmit power.

(ii) Seasaw: Most of you have played on the seesaw. Since there is a difference in the weight of the persons sitting on it, the heavier person lifts the lighter person. When the heavier person comes closer to the pivot point (fulcrum) the distance of the line of action of the force decreases. It causes less amount of torque to act on it. This enables the lighter person to lift the heavier person.

(iii) Steering Wheel: A small steering wheel enables you to manoeuvre a car easily by transferring torque to the wheels with less effort.

Question 2.
State Newton’s third law. Explain it with three examples.
Answer:
Newton’s third law of motion: Newton’s third law states that ‘for every action, there is an equal and opposite reaction. They always act in two different bodies’.
If a body A applies a force F_A on a body B, then the body B reacts with force F_B on the body A, which is equal to F_A in magnitude, but opposite in direction.
F_B = -F_A
Examples:

• When birds fly they push the air downwards with their wings (Action) and the air pushes the bird upwards (Reaction).
• When a person swims he pushes the water using the hands backwards (Action), and the water pushes the swimmer in the forward direction (Reaction).
• When you fire a bullet, the gun recoils backwards and the bullet is moving forward (Action) and the gun equalises this forward action by moving backwards (Reaction).

Question 3.
Derive the relation between ‘g’ and G. Explain how to determine the mass of earth.
Answer:
(i) Let us compute the magnitude of this force in two ways. Let, M be the mass of the Earth and m be the mass of the body.
(ii) The entire mass of the Earth is assumed to be concentrated at its centre.
(iii) The radius of the Earth is R = 6378 km (= 6400 km approximately). By Newton’s law of gravitation, the force acting on the body is given by
\(\mathrm{F}=\frac{\mathrm{GM} m}{\mathrm{R}^{2}}\) ….(1)

(iv) The radius of the body considered is negligible when compared with the Earth’s radius. Now, the same force can be obtained from Newton’s second law of motion.
(v) According to this law, the force acting on the body is given by the product of its mass and acceleration (called weight). Here, acceleration of the body is under the action of gravity hence a = g
F = ma = mg
F = weight = mg ……. (2)
Comparing equations J = F × t and ΔP = F × t, we get
\(m g=\frac{G M m}{R^{2}}\) …….. (3)
Acceleration due to gravity
\(g=\frac{\mathrm{GMm}}{\mathrm{R}^{2}}\) ……. (4)
Mass of the Earth (M):
Rearranging the equation (4), the mass of the Earth is obtained as follows:
Mass of the Earth M = g R² / G
Substituting the known values of g, R and G, you can calculate the mass of the Earth as M = 5.972 × 10²⁴ kg.

VIII. Problems.

Question 1.
A cricket ball of mass 0.5 kg strikes a bat normally with a velocity of 30 ms^-1 and rebounds with a velocity of 20 ms^-1 in the opposite direction, calculate the impulse of the force exerted by the ball on the bat.
Solution:
Impulse = change in momentum = mu – (-mv)
= m (u + v)
= 0.5 (30 + 20)
= 25 Ns

Question 2.
A force exerted on a body of mass 100 g changes its speed by 0.2 ms^-1 in each second. Calculate the magnitude of the force.
Given, mass m = 100 g = 0.1 kg and acceleration a = 200 cms^-2 = 0.2 ms^-2.
Solution:
F = ma = 0.1 × 0.2 = 0.02 N.

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Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 8 Statistics and Probability Ex 8.3

10th Maths Exercise 8.3 Samacheer Kalvi Question 1.
Write the sample space for tossing three coins using tree diagram.
Solution:

Ex 8.3 Class 10 Samacheer Question 2.
Write the sample space for selecting two balls from a bag containing 6 balls numbered 1 to 6 (using tree diagram).
Solution:

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Exercise 8.3 Class 10 Samacheer Question 3.
If A is an event of a random experiment such that P(A) : P(\(\overline{\mathbf{A}}\)) =17 : 15 and n(S) = 640 then find
(i) P(\(\overline{\mathbf{A}}\))
(ii) n(A).
Solution:
P(A): P(\(\overline{\mathbf{A}}\)) = 17 : 15

10th Maths 8.3 Solutions Question 4.
A coin is tossed thrice. What is the probability of getting two consecutive tails?
Solution:
Outcomes {O}: {(HHH), (THH), (HTH), (HHT), (HTT), (THT), (TTH), (TTT)}
Two consecutive tails {F} : {(HTT), (TTH), (TTT)}
n{F} = 3
n{O} = 8

10th Maths Exercise 8.3 Question 5.
At a fete, cards bearing numbers 1 to 1000, one number on one card are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square number greater than 500, the player wins a prize. What is the probability that
(i) the first player wins a prize
(ii) the second player wins a prize if the first has won?
Answer:
Sample space = {1, 2, 3,… ,1000}
n(S) = 1000
(i) Let A be the event of setting square number greater than 500
A = {529, 576, 625, 676, 729, 784, 841, 900, 961}
n(A) = 9
P(A) = \(\frac{n(\mathrm{A})}{n(\mathrm{S})}=\frac{9}{1000}\)
The probability that the first player wins prize = \(\frac{9}{1000}\)
(ii) If the first player wins, the number is excluded for the second player.
n(A) = 8 and n(S) = 999
P(A) = \(\frac{n(A)}{n(S)}=\frac{8}{999}\)
Probability the second player wins a prize = \(\frac{8}{999}\)

10th Maths Probability Exercise 8.3 Question 6.
A bag contains 12 blue balls and x red balls. If one ball is drawn at random
(i) what is the probability that it will be a red ball?
(ii) If 8 more red balls are put in the bag, and if the probability of drawing a red ball will be twice that of the probability in (i), then find x.
Solution:
12 ➝ blue balls
x ➝ red balls
(i) P (red ball) = \(\frac{x}{x+12}\)
(ii) 8 red balls are added to the bag.
∴ 12 ➝ blue balls
x + 8 ➝ red balls

Given that P(ii) = 2 × P(i)

⇒ (x + 8)(x + 12) = 2x(x + 20)
⇒ (x² + 20x + 96) = 2x² + 40x
⇒ x² + 20x – 96 = 0
⇒ x² + 24x – 4x – 96 = 0
⇒ x(x + 24) – 4(x + 24) = 0
⇒ (x – 4)(x + 24) = 0
∴ x = 4 (or) x = -24
x cannot be negative ⇒ x = 4
Substituting x = 4 in (i),

10th Maths Exercise 8.3samacheer Kalvi Question 7.
Two unbiased dice are rolled once. Find the probability of getting
(i) a doublet (equal numbers on both dice)
(ii) the product as a prime number
(iii) the sum as a prime number
(iv) the sum as 1
Solution:
Doublet = {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6,6)}
Total number of outcomes = 6 × 6
n(S) = 36
Number of favourable outcomes = 6

(ii) Number of favourable outcomes = 6
as favourable outcomes = (1, 2), (2, 1), (1, 3), (3, 1),(1, 5),and (5, 1)

(iii) Sum as prime numbers = {(1, 1), (1, 2), (2, 3), (1, 4), (1, 6), (4, 3), (5, 6)}
Number of favourable outcomes = 7
⇒ Probability = \(\frac{7}{36}\)

(iv) With two dice, minimum sum possible = 2
∴ Prob (sum as 1) = 0 [Impossible event]

10th Maths 8.3 Question 8.
Three fair coins are tossed together. Find the probability of getting
(i) all heads
(ii) atleast one tail
(iii) atmost one head
(iv) atmost two tails
Answer:
Three fair coins are tossed together
Sample spade = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
n(S) = 8
(i) Let A be the event of getting all heads
A = {HHH}
n(A) = 1
\(P(A)=\frac{n(A)}{n(S)}=\frac{1}{8}\)
(ii) Let B be the event of getting atleast one tail.
B = {HHT, HTH, HTT, THH, THT, TTH, TTT}
n(B) = 7
\(P(B)=\frac{n(B)}{n(S)}=\frac{7}{8}\)
(iii) Let C be the event of getting atmost one head
C = {HTT, THT, TTH, TTT}
n(C) = 4
\(P(C)=\frac{n(C)}{n(S)}=\frac{4}{8}=\frac{1}{2}\)
(iv) Let D be the event of getting atmost two tails.
D = {HTT, TTT, TTH, THT, THH, HHT, HTH}
n(D) = 7
\(P(D)=\frac{n(D)}{n(S)}=\frac{7}{8}\)

10 Maths Exercise 8.3 Question 9.
Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3 respectively. They are rolled and the sum of the numbers on them is noted. Find the probability of getting each sum from 2 to 9 separately.
Solution:
Dice 1
S = {1,2, 3, 4, 5, 6}
Dice 2
S = {1,1,2, 2, 3, 3}
Total possible outcomes when they are rolled

n(S) = 36
Event of sum (2) = A = {(1,1), (1,1)},
n(A) = 2,P(A) = \(\frac{2}{36}\)
Event of sum 3 is B = {(1, 2), (1, 2), (2, 1), (2, 1)}

Event of sum 4 is C= {(1, 3), (1, 3), (2, 2), (2, 2), (3, 1) (3, 1)}
n(C) = 6

Event of getting the sum 5 is
D = {(2, 3), (2, 3), (3, 2), (3, 2), (4, 1), (4, 1)}
n(D) = 6, P(D) = \(\frac{6}{36}\) .
Event of getting the sum 6 is
E = {(3, 3), (3, 3), (4, 2), (4, 2), (5, 1), (5, 1)}
n(E) = 6, P(E) = \(\frac{6}{36}\)
Event of getting the sum 7 is
F = {(4, 3), (4, 3), (5, 2), (5, 2), (6, 1), (6, 1)}
n(F) = 6
P(F) = \(\frac{6}{36}\)
Event of getting the sum 8 is
G = {(5, 3), (5, 3), (6, 2), (6, 2)}

Event of getting the sum 9 is
H = {(6, 3), (6, 3), n(H) = 2

10th Standard Maths Exercise 8.3 Question 10.
A bag contains 5 red balls, 6 white balls, 7 green balls, 8 black balls. One ball is drawn at random from the bag. Find the probability that the ball is drawn
(i) white
(ii) black or red
(iii) not white
(iv) neither white nor black
Solution:
5 red 6 white 7 green 8 black total no. of balls = 5 + 6 + 7 +8= 26

Exercise 8.3 Class 10 Samacheer Kalvi Question 11.
In a box there are 20 non-defective and some defective bulbs. If the probability that a bulb selected at random from the box found to be defective is 3/8 then, find the number of defective bulbs.
Solution:
Let number of defective bulbs be ‘x’
Total number of bulbs = x + 20

⇒ 8x = 3x + 60
⇒ 5x = 60
⇒ x = 12
∴ No.of defective bulbs are = 12.

10th Maths Exercise 8.4 Samacheer Kalvi Question 12.
The king and queen of diamonds, queen and jack of hearts, jack and king of spades are removed from a deck of 52 playing cards and then well shuffled. Now one card is drawn at random from the remaining cards. Determine the probability that the card is
(i) a clavor
(ii) a queen of red card
(iii) a king of black card
Solution:

(i.e) remaining number of cards = 52 – 6 = 46 13
(i) P(a clavor) = \(\frac{13}{46}\)
(ii) P(queen of red card) = 0 as both Queen of diamond and heart have been removed.
(iii) only K of clavor is in the deck
⇒ P(king of black card) = \(\frac{1}{46}\)

10th Maths Ex 8.3 Question 13.
Some boys are playing a game, in which the stone was thrown by them landing in a circular region (given in the figure) is considered as a win and landing other than the circular region is considered as a loss. What’is the probability to win the game?

Solution:

Samacheer Kalvi 10th Maths Exercise 8.3 Question 14.
Two customers Priya and Amuthan are visiting a particular shop in the same week (Monday to Saturday). Each is equally likely to visit the shop on any one day as on another day. What is the probability that both will visit the shop on
(i) the same day
(ii) different days
(iii) consecutive days?
Solution:

10th Maths Exercise 8.3 4th Sum Question 15.
In a game, the entry fee is ₹ 150. The game consists of tossing a coin 3 times. Dhana bought a ticket for entry. If one or two heads show, she gets her entry fee back. If she throws 3 heads, she receives double the entry fees. Otherwise, she will lose. Find the probability that she
(i) gets double entry fee
(ii) just gets her entry fee
(iii) loses the entry fee.
Solution:

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Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 5 Coordinate Geometry Ex 5.2

10th Maths Exercise 5.2 Samacheer Kalvi Question 1.
What is the slope of a line whose inclination with positive direction of x -axis is
(i) 90°
(ii) 0°
Solution:
(i) θ = 90°
m = tan θ = tan 90° = ∝ (undefined)
(ii) m = tan θ = tan 0° = 0

Exercise 5.2 Class 10 Samacheer Kalvi Question 2.
What is the inclination of a line whose slope is (i) 0
Solution:
(i) Slope = 0
tan θ = 0
tan 0 = 0
∴ θ = 0°

(ii) Slope = 1
tan θ = 1
tan 45° = 1
∴ θ = 45°
angle of inclination is 45°

Ex 5.2 Class 10 Samacheer Question 3.
Find the slope of a line joining the points
(i) (5, \(\sqrt{5})\)) with origin
(ii) (sin θ, -cos θ) and (-sin θ, cos θ)
(i) (5, \(\sqrt{5})\)) with origin (0, 0)
Solution:

10th Maths Exercise 5.2 Question 4.
What is the slope of a line perpendicular to the line joining A(5, 1) and P where P is the mid-point of the segment joining (4, 2) and (-6,4).
Solution:
P is the mid point of the segment joining (4, 2) and (-6, 4)

10th Maths Ex 5.2 Question 5.
Show that the given points are collinear (-3, -4), (7, 2) and (12, 5)
Solution:
The verticles are A(-3, -4), B(7, 2) and C (12, 5)

Slope of AB = Slope of BC
∴ The points A, B and C lie on the same line.
∴ They are collinear.

10th Maths Exercise 5.2 Solution Question 6.
If the three points (3, -1), (a, 3), (1, -3) are collinear, find the value of a.
Solution:
Slope of AB = slope of BC.

Samacheer 10th Maths Exercise 5.2 Solutions Question 7.
The line through the points (-2, a) and (9, 3) has slope –\(\frac{1}{2}\). Find the value of a.
Solution:
A line joining the points (-2, a) and (9, 3) has slope m = –\(\frac{1}{2}\).

10th Maths Coordinate Geometry Exercise 5.2 Question 8.
The line through the points (-2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24) . Find the value of x.
Solution:

10th Maths Exercise 5.2 In Tamil Question 9.
Show that the given points form a right angled triangle and check whether they satisfies pythagoras theorem
(i) A(1, -4), B(2, -3) and C(4, -7)
(ii) L(0, 5), M(9, 12) and N(3, 14)
Solution:

10th Coordinate Geometry 5.2 Question 10.
Show that the given points form a parallelogram : A(2.5, 3.5), B(10, -4), C(2.5, -2.5) and D(-5, 5)
Solution:



∴ The given points form a parallelogram.

10th Maths 5.2 Exercise Question 11.
If the points A(2, 2), B(-2, -3), C(1, -3) and D(x, y) form a parallelogram then find the value of x and y.
Solution:
A(2, 2), B(-2, -3), C(1, -3), D(x, y)

Since ABCD forms a parallelogram, slope of opposite sides are equal and diagonals bisect each other.
Mid point of BD = Mid point of AC

10th Maths 5.2 Question 12.
Let A(3, -4), B(9, -4), C(5, -7) and D(7, -7). Show that ABCD is a trapezium.
Solution:
A (3, -4), B (9, -4), C (5, -7) and D (7, -7)

If only one pair of opposite sides of a quadrilateral are parallel, then it is said to be a trapezium.


∴ One pair of opposite sides are parallel.
∴ ABCD is a trapezium.

Samacheer Kalvi 10th Maths Exercise 5.2 Question 13.
A quadrilateral has vertices at A(- 4, -2), B(5, -1) , C(6, 5) and D(-7, 6). Show that the mid-points of its sides form a parallelogram
Solution:




In a parallelogram diagonals bisect each other. Opposite sides are parallel as their slopes are equal the mid points of the diagonals are the same.
∴ Mid points of the sides of a quadrilateral form a parallelogram.

10th Exercise 5.2 Question 14.
PQRS is a rhombus. Its diagonals PR and QS intersect at the point M and satisfy QS =2PR. If the coordinates of S and M are (1, 1) and (2, -1) respectively, find the coordinates of P.
Solution: