## Samacheer Kalvi 9th Maths Guide Chapter 2 Real Numbers Ex 2.2

Students can download Maths Chapter 2 Real Numbers Ex 2.2 Questions and Answers, Notes, Samacheer Kalvi 9th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 2 Real Numbers Ex 2.2

Therefore, one Decimal is equal to four hundred and thirty five decimal point six Square Feet (sq ft) in Online.

Question 1.
Express the following rational numbers into decimal and state the kind of decimal expression.
(i) $$\frac{2}{7}$$
(ii) -5$$\frac{3}{11}$$
(iii) $$\frac{22}{3}$$
(iv) $$\frac{327}{200}$$
Solution:

(i) $$\frac{2}{7}$$ = 0.2857142….
= 0.$$\overline {285714}$$
Non-terminating and recurring decimal expansion.

(ii) -5$$\frac{3}{11}$$ = -5 + 0.272 = -5.272……..

= -5.$$\overline {27}$$
Non-terminating and recurring decimal expansion.

(iii) $$\frac{22}{3}$$ = 7.333……..

= 7.$$\overline {3}$$
Non-terminating and recurring decimal expansion.

(iv) $$\frac{327}{200}$$ = $$\frac{327}{2×100}$$

= $$\frac{3.27}{2}$$
= 1.635
Terminating decimal expansion.

How to convert 1/32 to decimal form? … In the fraction 1/32, 1 is the numerator and 32 is the denominator, the fraction bar means “divided by”.

Question 2.
Express $$\frac{1}{13}$$ in decimal form. Find the length of the period of decimals.
Solution:

$$\frac{1}{13}$$ = 0.07692307
= 0.$$\overline {076923}$$
Length of the period of decimal is 6.

9/20 as a decimal is 0.45

Question 3.
Express the rational number $$\frac{1}{33}$$ in recurring decimal form by using the recurring decimal expansion of $$\frac{1}{11}$$. Hence write $$\frac{71}{33}$$ in recurring decimal form.
Solution:

$$\frac{1}{11}$$ = 0.0909……… = 0.$$\overline {09}$$
∴ $$\frac{1}{33}$$ = $$\frac{1}{3}$$ × $$\frac{1}{11}$$
= $$\frac{1}{3}$$ × 0.0909 ……..
= 0.0303 …… = 0.$$\overline {03}$$
$$\frac{71}{33}$$ = 2$$\frac{5}{33}$$ = 2 + $$\frac{5}{33}$$ = 2 + 5 × $$\frac{1}{33}$$
= 2 + 5 × 0.$$\overline {03}$$
2 + (5 × 0.030303 ……..)
2 + 0.151515 ………
2+ 0.$$\overline {15}$$
2.$$\overline {15}$$

That’s literally all there is to it! 1/2 as a decimal is 0.5.

Question 4.
Express the following decimal expression into rational numbers.
(i) 0.24
Solution:
Let x = 0.242424 ………. →(1)
100 x = 24.2424 ……… →(2)
(2) – (1) ⇒ 100 x – x = 24.2424 ……….. (-)
0.2424 ……..
99 x = 24.0000
x = $$\frac{24}{99}$$
(or)
$$\frac{8}{33}$$

(ii) 2.327
Solution:
Let x = 2.327327327 ………. →(1)
1000 x = 2327.327327 ……… →(2)
(2) – (1) ⇒ 1000 x – x = 2327.327327 ……….. (-)
2.327327 ……..
999 x = 2325.000
x = $$\frac{2325}{999}$$
(or)
$$\frac{775}{333}$$

(iii) – 5.132
Solution:
– 5.132 = -5 + $$\frac{1}{10}$$ + $$\frac{3}{100}$$ + $$\frac{2}{1000}$$
= $$\frac{-5000 + 100 +30 + 2}{1000}$$ = $$\frac{-4868}{1000}$$
(or)
$$\frac{-1217}{250}$$

(iv) 3.17
Solution:
Let x = 3.1777 ………. →(1)
10 x = 31.777 ……… →(2)
100 x = 317.77 …….. →(3)
(3) – (2) ⇒ 100 x – 10 x = 317.77 ……….. (-)
31.777 ……..
90 x = 286.000
x = $$\frac{286}{90}$$
(or)
$$\frac{143}{45}$$

(v) 17.215
Solution:
Let x = 17.2151515 ………. →(1)
10 x = 172.151515 ……… →(2)
100 x = 17215.1515 …….. →(3)
(3) – (2) ⇒ 1000 x – 10 x = 17215.1515 ……….. (-)
17215.1515 ……..
990 x = 17043
x = $$\frac{17043}{990}$$
(or)
$$\frac{5681}{330}$$

(vi) -21.2137
Solution:
Let x = -21.213777 ………. →(1)
1000 x = -21213.777 ……… →(2)
100 x = -212137.77 …….. →(3)
(3) – (2) ⇒ 10000 x – 1000 x = -21213.777 ……….. (-)
-21213.777 ……..
9000 x = -190924
x = $$\frac{-190924}{9000}$$
(or)
$$\frac{-47731}{2250}$$

That’s literally all there is to it! 11/16 as a decimal is 0.6875.

Question 5.
Without actual division, find which of the following rational numbers have terminating decimal expression.
(i) $$\frac{7}{128}$$
Solution:

$$\frac{7}{128}$$ = $$\frac{7}{2^{7}}$$
∴ $$\frac{7}{128}$$ has terminating decimal expression.

(ii) $$\frac{21}{15}$$
Solution:
$$\frac{21}{15}$$ = $$\frac{7}{5}$$ = $$\frac{7}{5^1}$$
$$\frac{21}{15}$$ has terminating decimal expression.

(iii) 4$$\frac{9}{35}$$
Solution:
4$$\frac{9}{35}$$ = $$\frac{149}{35}$$
4$$\frac{149}{5×7}$$ (It is not in the form of $$\frac{P}{2^{m} × 5^{n}}$$
∴ 4$$\frac{9}{35}$$ has non-terminating recurring decimal expression.

(iv) $$\frac{219}{2200}$$
Solution:

$$\frac{219}{2200}$$ = $$\frac{219}{2^{3} × 5^{2} × 11}$$ (It is not in the form of $$\frac{P}{2^{m} × 5^{n}}$$
∴ $$\frac{219}{2200}$$ has non-terminating recurring decimal expression.

## Samacheer Kalvi 9th Maths Guide Chapter 3 Algebra Ex 3.8

Students can download Maths Chapter 3 Algebra Ex 3.8 Questions and Answers, Notes, Samacheer Kalvi 9th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 3 Algebra Ex 3.8

Synthetic division calculator. This calculator divides two polynomials using synthetic division.

Question 1.
Factorise each of the following polynomials using synthetic division:
(i) x3 – 3x² – 10x + 24
Solution:
p(x) – x3 – 3x² – 10x + 24
p(1) = 13 – 3(1)² – 10(1) + 24
= 1 – 3 – 10 + 24
= 25 – 13
≠ 0
x – 1 is not a factor

p(-1) = (-1)3 – 3(-1)² – 10(-1) + 24
= – 1 – 3(1) + 10 + 24
= -1 – 3 + 10 + 24
= 34 – 4
= 30
≠ 0
x + 1 is not a factor

p(2) = 23 – 3(2)² – 10(2) + 24
= 8 – 3(4) – 20 + 24
= 8 – 12 – 20 + 24
= 32 – 32
= 0
∴ x – 2 is a factor

x² – x – 12 = x² – 4x + 3x – 12

= x(x – 4) + 3 (x – 4)
= (x – 4) (x + 3)
∴ The factors of x3 – 3x² – 10x + 24 = (x – 2) (x – 4) (x + 3)

(ii) 2x3 – 3x² – 3x + 2
Solution:
p(x) = 2x3 – 3x² – 3x + 2
P(1) = 2(1)3 – 3(1)² – 3(1) + 2
= 2 – 3 – 3 + 2
= 2 – 6
= -4
≠ 0
x – 1 is not a factor

P(-1) = 2(-1)3 – 3(-1)² – 3(-1) + 2
= -2 – 3 + 3 + 2
= 5 – 5
= 0
∴ x + 1 is a factor

2x² – 5x + 2 = 2x² – 4x – x + 2

= 2x(x – 2) – 1 (x – 2)
= (x – 2) (2x – 1)
∴ The factors of 2x3 – 3x² – 3x + 2 = (x + 1) (x – 2) (2x – 1)

(iii) – 7x + 3 + 4x3
Solution:
p(x) = – 7x + 3 + 4x3
= 4x3 – 7x + 3
P(1) = 4(1)3 – 7(1) + 3
4 – 7 + 3
= 7 – 7
= 0
∴ x – 1 is a factor

4x² + 4x – 3 = 4x² + 6x – 2x – 3

= 2x(2x + 3) – 1 (2x + 3)
= (2x + 3) (2x – 1)
∴ The factors of – 7x + 3 + 4x3 = (x – 1) (2x + 3) (2x – 1)

(iv) x3 + x² – 14x – 24
Solution:
p(x) = x3 + x² – 14x – 24
p(1) = (1)3 + (1)2 – 14 (1) – 24
= 1 + 1 – 14 – 24
= -36
≠ 0
x + 1 is not a factor.

p(-1) = (-1)3 + (-1)² – 14(-1) – 24
= -1 + 1 + 14 – 24
= 15 – 25
≠ 0
x – 1 is not a factor.

p(2) = (-2)3 + (-2)2 – 14 (-2) – 24
= -8 + 4 + 28 – 24
= 32 – 32
= 0
∴ x + 2 is a factor

x² – x – 12 = x² – 4x + 3x – 12

= x(x – 4) + 3 (x – 4)
= (x – 4) (x + 3)
This (x + 2) (x + 3) (x – 4) are the factors.
x3 + x2 – 14x – 24 = (x + 2) (x + 3) (x – 4)

(v) x3 – 7x + 6
Solution:
p(x) = x3 – 7x + 6
P( 1) = 13 – 7(1) + 6
= 1 – 7 + 6
= 7 – 7
= 0
∴ x – 1 is a factor

x² + x – 6 = x² + 3x – 2x – 6

= x(x + 3) – 2 (x + 3)
= (x + 3) (x – 2)
This (x – 1) (x – 2) (x + 3) are factors.
∴ x3 – 7x + 6 = (x – 1) (x – 2) (x + 3)

(vi) x3 – 10x² – x + 10
p(x) = x3 – 10x2 – x + 10
= 1 – 10 – 1 + 10
= 11 – 11
= 0
∴ x – 1 is a factor

x2 – 9x – 10 = x2 – 10x + x – 10

= x(x – 10) + 1 (x – 10)
= (x – 10) (x + 1)
This (x – 1) (x + 1) (x – 10) are the factors.
∴ x3 – 10x2 – x + 10 = (x – 1) (x – 10) (x + 1)

## Samacheer Kalvi 9th Social Science Guide Civics Chapter 4 Forms of Government

Tamilnadu State Board New Syllabus Samacheer Kalvi 9th Social Science Guide Pdf Civics Chapter 4 Forms of Government Text Book Back Questions and Answers, Important Questions, Notes.

## Tamilnadu Samacheer Kalvi 9th Social Science Solutions Civics Chapter 4 Forms of Government

### Samacheer Kalvi 9th Social Science Forms of Government Text Book Back Questions and Answers

I. Fill in the blanks

1. _________, __________ are a few examples for unitary form of government.
2. The parliamentary government is also known as __________
3. In the parliamentary fonn of government __________is the leader of the majority party.

1. England, France
2. Cabinet government
3. Prime Minister

II. Fill in the blanks

Question 1.

 S.No Country Name of the parliament 1. USA ………………………….. 2. Norway ………………………….. 3. …………………………… Folketing

 S.No Country Name of the parliament 1. USA Congress 2. Norway Storting 3. Denmark Folketing

III. Distinguish Between

The KTM full form is Kraftfahrzeuge Trunkenpolz Mattighofen, and KTM full form in English translation is ‘motor vehicle’.

Question 1.
Unitary and federal forms of government. Ans
Unitary form of government:

1. Only one level of government or sub units
2. Subunits cannot operate independently
3. E.g. England, France, Japan, Srilanka

Federal form of government:

1. Two levels of government
2. Federal units are answerable to central government

Question 2.
Parliamentary and presidential forms of government.
Parliamentary form of government:

1. Prime Minister is the leader of the majority party.
2. Central Legislature is supreme E.g.Canada, India, Japan

Presidential form of government:

1. President is directly selected by the people.
2. President is supreme E.g. Rassia, Brazil, U.S.A

IV. Give a short note on

Question 1.
Unitary form of government
A unitary system of government or unitary state is a sovereign state governed as a single entity. The central government is supreme and the administrative divisions exercise only powers that the central government has delegated to them. England, France, Japan and Sri Lanka are examples of the Unitary Form of government. In a Unitary form of government, all the authority and power is vested in a single-center, whereas in a federal form of government authority and power is distributed between the center and the constituent units. Even in a Unitary form of Government, there might be a lot of decentralization of authority, but we cannot claim it as a federal system.

Question 1.
List out the types of constitution.
Types of Constitution

Question 2.
What are the merits of a federal government?
The merits of the federal government are

1. Reconciliation of local autonomy with national unity.
3. It gives rise to big states.
4. Distribution powers check the despotism of central government.
5. More suitable for bigger countries
6. It is good for economic and cultural progress.

Question 3.
Write down the differences between the unitary form of government and the federal form of government.
Unitary form of government:

1. Only one Level of Government or subunits
2. Mostly Single Citizenship
3. Sub Units cannot operate Independently
4. No Division of Power
5. Centralization of Power

The federal form of government:

1. Two Levels of Government
2. Dual Citizenship
3. Federal Units are answerable to Central Government
4. Division of Power
5. Decentralization of Power

Question 1.
Write about the merits of a unitary form of government
Merits of a unitary form of government

• Suitable for small countries.
• There is no conflict between authority and responsibility.
• A unitary government will make prompt decisions and take speedy action.
• A unitary government is less expensive.
• Amendments to the constitution are easy.
• There is unity, uniformity of law, policy, and administration.

Question 2.
Write about the presidential form of government and what is the difference between presidential and parliamentary forms of government.
Presidential form of government:

1. The American President is both the head of the state and the head of government. As the head of state, he occupies a ceremonial position.
2. The president is elected by an electoral college for a fixed tenure of four years.
3. He governs with the help of a cabinet or a smaller body called ‘Kitchen Cabinet’. It is only an advisory body.
4. The President and his secretaries are not responsible to Congress for their acts.
5. The legislative, executive and judicial powers of the government are separated.
6. It is also known as the non-responsible or non-parliamentary or fixed executive system of government.

Difference between Presidential and Parliamentary form of government Presidential Form of Government:

1. President is directly elected by the people.
2. President is supreme
3. Separation of Powers
4. Independent branches
6. Separation of Powers
7. Independent branches
9. President is not accountable to Congress

Parliamentary form of Government:

1. Prime Minister is the leader of the majority party.
2. Central Legislature is supreme
3. Absence of Separation Powers Centralisatiion
4. Independent branches with Overlapping functions
5. Prime Minister-head of the Government
6. Centralisation
7. Independent branches with Overlapping functions
9. Collective and Individual Responsibility.

### Samacheer Kalvi 9th Social Science Forms of Government Additional Important Questions and Answers

I. Fill in the blanks.

1. The government in the main ______ of the state.
2. There are ______ organs in a Government.
3. Sri Lanka is an example of ______ form of government.
4. Unitary form of government suitable ______ for Countres.
5. U.S. represents form, ______ of government.
6. The constitution is the ______ of the land.
7. The Name of the Parliament in Israel in ______
8. In India we have ______ form government.
9. Brazil has ______ form of governments.
10.  In Bhutan king Jigme is a ______ monarch.
11. The Gross National Happiness (GNH) was first mentioned in the constitution of ______
12. The term GNH was coined by ______

1. Agency
2. Three
3. unitary
4. small
5. Federal
6. Supreme law
7. Knesset
8. Parliamentary
9. Presidential
10. Constitutional
11. Bhutan
12. Jigme Singye Wangchuck – King of Bhutan

II. Fill in the blanks

Question 1.

 S.No Country Name of the Parliment 1. Israel ………………………… 2. Germany …………………………

 S.No Country Name of the Parliment 1. Israel ………………………… 2. Germany …………………………

III. Distinguish Between

Question 1.
Dictatorship and Monarality
Dictatorship

1. Dictatorship is an office that has been taken through force.
2. A Dictatorship is termed as a government rule by one person or commands who is know as the Dictator. E.g. Uganda, Zimbawe

Monarchy

1. Monarchy is resigned that passed from one generation to another.
2. Monarchy is the rule of the king or green as an emperor. E.g. Britain, Australia.

Question 2.
Democracy and Communism
Democracy:

1. Democracy is based on the principle of equality and Freedom.
2. Private ownership is allowed citizens; have certain legislature and freedom which are protected by the constitution, E.g. India.

Communism:

1. Communism is based on common ownership mainly concerned with equality and fairness.
2. Here the government has complete control over the production and distribution of goods and all the resources shared equally in the society. E.g. China, North Korea.

IV. Give a short note on

Question 1.
Historic Transition in Bhutan.

1. The fourth king of Bhutan Jigme Singye Wangchuck travelled to all the 20 districts of the tiny kingdom.
2. The purpose of the travel is to explain the importance of the historic transition to the people of Bhutan.
3. The transition from the hereditary monarchy to the Parliamentary Democracy.
4. In 2006 the king abdicated the throne 34 years after ascending it. Now Bhutan is a Parliamentary Democracy and King Jigme a constitutional monarch.

Question 2.
What are the characteristics of good governance?
Characteristics of Good governance

1. Participation
2. Rule of Law
3. Transparency
4. Responsiveness
5. Consensus Orientation
6. Equity
7. Effectiveness And Efficiency
8. Accountability

Question 1.
What are the demerits of federal form government?
De-merits of the federal form of government are,

1. Federal government is weaker when compared to the unitary government.
2. Federal government is more expensive.
3. Provincial tendencies are very common
4. Lack of uniformity in Administration
5. Threat to national unity
6. Distribution powers between centre and states lead to conflict
7. Double Citizenship
8. Rigid constitution cannot be amended easily for the changing needs.
9. The state governments sometimes place hindrances in foreign policy.

Question 2.
Mention about the Unitary features of Indian constitution
Unitary features of Indian constitution are

1. Strong Centre
2. Central Government’s control over state territory
3. Single Constitution
4. The flexibility of the Constitution
5. Unequal representation of states
6. Emergency Provisions
7. Single citizenship
8. Single Integrated Judiciary
9. All India Services
10. Appointment of Governor by the central government.

Question 3.
What are the Federal features of the Indian constitution?
Federal features of the Indian constitution are

1. Dual Government
2. Written constitution
3. Division of Powers
4. The supremacy of the Constitution
5. the constitution is the supreme law of the land.
6. The laws enacted by the Centre and the states must conform to its provisions.
7. Rigid Constitution
8. Independent Judiciary
9. Bicameralism

Question 4.
Write about the demerits of a unitary form of government
De-merits of a unitary form of government

1. It is not suitable for big countries.
2. The central government will have to tackle so many complex problems that lead to administrative delays.
3. The central government will not concentrate on local problems, local interest and initiative.
4. The concentration of powers .may pave way for the despotism of the central government.

Question 1.
Write note the Parliamentary form of Government
Parliamentary form of Government:

1. The parliamentary system of government is the one in which the executive is responsible to the legislature for its policies and acts.
2. It is also known as cabinet government or responsible government or Westminister model of government and is prevalent in Britain, Japan, Canada, India among others.

Features of Parliamentary form of government:

1. Nominal and Real Executives.
2. Majority Party Rule
3. Collective Responsibility
4. Double Membership
5. The leadership of the Prime Minister

Merits of the parliamentary form of government:

1. Harmony between Legislature and Executive.
2. Responsible Government
3. Prevents Dictatorship.
4. Wide Representation.

Demerits of the parliamentary form of government:

1. Unstable Government.
2. No Continuity of Policies.
3. The dictatorship of the Cabinet.
4. Against Separation of Powers.

## Samacheer Kalvi 9th Science Guide Chapter 1 Measurement

Tamilnadu State Board New Syllabus Samacheer Kalvi 9th Science Guide Pdf Chapter 1 Measurement Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 9th Science Solutions Chapter 1 Measurement

### 9th Science Guide Measurement Text Book Back Questions and Answers

I. Choose the correct answer :

Question 1.
Choose the correct one.
(a) mm < cm < m < km
(b) mm > cm > m > km
(c) km < m < cm < mm
d) mm > m > cm > km
(a) mm < cm < m < km

Question 2.
Rulers, measuring tapes and metre scales are used to measure
(a) mass
(b) weight
(c) time
(d) length
(d) length

Question 3.
1 metric ton is equal to
(a) 100 quintals
(b) 10 quintals
(c) 1/10 quintals
(d) 1/100 quintals
(b) 10 quintals

Question 4.
Which among the following is not a device to measure mass?
(a) Spring balance
(b) Beam balance
(c) Physical balance
(d) Digital balance
(a) Spring balance

II. Fill in the blanks :

1. Metre is the unit of …………..
length

2. 1 kg of rice is weighed by ……………
beam balance

3. Thickness of a cricket ball is measured by ……………..
vernier caliper

4. Radius of a thin wire is measured by …………………
screw gauge

5. A physical balance measures small differences in mass up to ……………….
1mg or less

III. State whether true or false. If false, correct the statement :

1. The SI unit of electric current is kilogram.
False.
Correct statement: The SI unit of electric current is ampere.

2. Kilometre is one of the SI units of measurement.
True.

3. In everyday life, we use the term weight instead of mass.
True.

4. A physical balance is more sensitive than a beam balance.
True.

5. One Celsius degree is an interval of IK and zero degree Celsius is 273.15 K.
True.

6 . With the help of vernier caliper we can have an accuracy of 0.1 mm and with screw gauge we can have an accuracy of 0.01 mm.
True.

IV. Match the following:

Question 1.

 Column I Column II Length kelvin Mass metre Time kilogram Temperature second

 Column I Column II Length metre Mass kilogram Time second Temperature kelvin

Question 2.

 Column I Column II Screw gauge Vegetables Vernier caliper Coins Beam balance Gold ornaments Digital balance Cricket ball

 Column I Column II Screw gauge Coins Vernier caliper Cricket ball Beam balance Vegetables Digital balance Gold ornaments

V. Assertion and reason type :

Mark the correct answer as :
(a) Both A and R are true but R is not the correct reason.
(b) Both A and R are true and R is the correct reason.
(c) A is true but R is false.
(d) A is false but R is true

Question 1.
Assertion (A) : The scientifically correct expression is “The mass of the bag is 10 kg”
Reason (R) : In everyday life, we use the term weight instead of mass.
(a) Both A and R are true but R is not the correct reason

Question 2.
Assertion (A) : 0° C = 273.16 K. For our convenience we take it as 273K after rounding off the decimal.
Reason (R) : To convert a temperature on the Celsius scale we have to add 273 to the given temperature.
(b) Both A and R are true and R is the correct reason

Question 3.
Assertion (A) : Distance between two celestial bodies is measured in terms of light year.
Reason (R) : The distance travelled by the light in one year is one light year.
(d) A is false but R is true
Distance between two celestial bodies is measured in terms of unit.

Question 1.
Define measurement.
Measurement is the process of comparison of the given physical quantity with the known standard quantity of the same nature.

Question 2.
Define a standard unit.
Unit is the quantity of a constant magnitude which is used to measure the magnitudes of other quantities of the same nature.

Question 3.
What is the full form of SI system?
The full form of S.I. system is the International System of Units.

Question 4.
Define least count of any device.
Least count is the least measurement possible in a given device.
It is the distance moved by the tip of the screw for a rotation of one division on the head scale.
Least count = [Pitch / No. of head scale divisions]

Question 5.
What do you know about pitch of screw gauge?
Pitch of the screw gauge is the distance between two successive screw threads. It is measured by the ratio of distance travelled on the pitch scale to the number of rotations of the head scale.

Question 6.
Can you find the diameter of a thin wire of length 2 m using the ruler from your instrument box?
No, I can not find the diameter of a thin wire of length 2 m using the ruler.

Question 1.
Write the rules that are followed in writing the symbols of units in SI system.

•  The units named after scientists are not written with a capital initial letter.
E.g. newton, henry, ampere, and watt.
• The symbols of the units named after scientists should be written by the initial capital letter.
E.g. N for newton, H for Henry, A for ampere, and W for watt.
• Small letters are used as symbols for units not derived from a proper noun.
E.g. m for metre, kg for kilogram.
•  No lull stop or other punctuation marks should be used within or at the end of symbols.
E.g. 50 m and not as 50 m.
•  The symbols of the units are not expressed in plural form.
E.g. 10 kg not as kgs.

Question 2.
Write the need of a standard unit.
A Standard Unit is needed to maintain uniformity in measurements like length, weight, size and distance. Eg: Standard Unit of length is metre.

Question 3.
Differentiate mass and weight.
Mass:

1.  Fundamental quantity
2.  Has magnitude alone – scalar quantity
3.  It is the amount of matter contained in a body
4.  Remains the same
5.  It is measured using physical balance
6.  Its unit is kilogram

Weight:

1.  Derived quantity
2.  Has magnitude and direction – vector quantity
3.  It is the normal force exerted by the surface on the object against gravitational pull
4.  Varies from place to place
5.  It is measured using spring balance
6.  Its unit is newton

Question 4.
How will you measure the least count of vernier caliper?
The least count of Vernier Caliper is the ratio of the value of one smallest main scale division to total
a number of Vernier scale divisions.
i.e., L.C. = 0.1mm = 0.01cm
(or) L.C. = 1MD – 1VSD = 1.0 mm – 0.9 mm = 0. 1mm = 0.01 cm

Question 1.
Explain a method to find the thickness of a hollow teacup.
Step 1 : The Pitch, Least count and the type of zero error of the screw gauge are determined.
Step 2 : The given cup is placed in between two studs.
Step 3 : The head screw using the ratchet arrangement is freely rotated until the given cup is held firmly, but not tightly.
Step 4 : Pitch scale reading (PSR) by the head scale and head scale coincidence (HSC) with the axis of the pitch scale, are found.
Step 5 : The readings are recorded and the experiment for different positions of the given cup is repeated.
Step 6 : The thickness of the cup is calculated using the formula P.S.R + (HSC × L.C)
Step 7 : Then the average of the last column of the table, is found. Hence the thickness of a hollow tea cup = ………….. mm.

Question 2.
How will you find the thickness of a one rupee coin?
Step 1 : The Pitch, Least count and the type of zero error of the screw gauge are determined.
Step 2 : The given coin is placed in between two studs.
Step 3 : The head screw using the ratchat arrangement is freely rotated until given one rupee coin is held firmly, but not tightly.
Step 4 : Pitch scale reading (PSR) by the head scale and head scale coincidence (HSC) with are axis of the pitch scale are found.
Step 5 : The reading are recorded and the experiment for different positions of the given coin is repeated.
Step 6 : The thickness of the coin is computed using the formula P.S.R + (HSC x L.C )
Step 7 : Then the average of the last column of the table is found.

mean = …………….. mm
Hence the thickness of a one rupee coin = ……………….. mm

IX. Numerical Problems :

Question 1.
Inian and Ezhilan argue about the light year. Inian tells that it is 9.46 x 1015m and Ezhilan argues that it is 9.46 x 1012 km. Who is right? Justify your answer.
(Inian is correct)
Light travels 3 × 108m in one second or 3 Lakhs kilometre in one second.
In one year we have 365 days.
The total number of second in one year is equal to 365 x 24 x 60 x 60
Distance travelled by light in 1 year = (3.153 x 107) x (3 x 108)
= 9.46 x 1015m

Question 2.
The main scale reading while measuring the thickness of a rubber ball using Vernier caliper is 7 cm and the Vernier scale coincidence is 6. Find the radius of the ball.
MSR = 7 cm
VC = 6cm
LC = 0.1mm = 0.1cm
Diameter = DR = MSR + (VC X LC)
= 7 + 0.06 cm
Diameter D = 7.06 cm
Radius R = $$\frac{D}{2}=\frac{7.06}{2}$$ = 0.035 m
The radius of the ball = 0.0353 m.

Question 3.
Find the thickness of a five rupee coin with the screw gauge, if the pitch scale reading is 1 mm and its head scale coincidence is 68.
PSR = 1 mm = 1 x 10-3m
HSC = 68
LC = 0.01 mm =0.01 × 10-3m
Total reading = PSR + (HSC × LC)
∴Thickness of the five rupee coin = 1 × 10-3 + (68 × 0.01 × 10-3 )m
∴ Thickness of the five rupee coin = 1.68 × 10-3m = 1.68mm

Question 4.
Find the mass of an object weighing 98 N.
W = mg
W =98 N
g = 9.8 m/s2
m = $$\frac{\mathrm{W}}{\mathrm{g}}=\frac{98}{9.8}$$ = 10 kg

Intext Activities

ACTIVITY – 1

Using Vernier caliper find the outer diameter of your pen cap.

Aim : To find the outer diameter of the pen cap.
Materials required : Vernier caliper, pen cap.

Result: The outer diameter of the pen cap = 9.35 cm
[End of the activity]

Class 7 Science MCQ Questions with answers.

ACTIVITY – 2

Determine the thickness of a single sheet of your science textbook with the help of a Screw gauge.

LC = Least Count
Result : The thickness of the single sheet = 0.30
End of the activity

I. Choose the correct answer :

Question 1.
Length is ……………….
(a) The amount of matter in an object
(b) The amount of space an object takes up.
(c) The distance between two points.
(d) The amount of stuff in an object
(c) The distance between two points

Question 2.
Mass is ………………….
(a) The distance between two points
(b) The distance between three points
(c) The amount of matter contained in an object
(d) The amount of space an object occupies.
(c)The amount of matter contained in an object

Question 3.
Unit used to measure length
(a) metre
(b) litre
(c) gram
(d) cubic metre (m3)
(a) metre

Question 4.
Unit which is used to measure mass
(a) ml
(b) 1
(c) cm
(d) gram
(d) gram

Question 5.
How many metres are there in 1 nanometer?
(a) 10-10m
(b) 10-9m
(c) 109m
(d) 1010m
(b) 10-9m

Question 6.
What unit will you use to measure the length of our classroom?
(a) km
(b) m
(c) cm
(d) mm
(b) m

Question 7.
The Kelvin is the basic unit of ………………..
(a) temperature
(b) mass
(c) length
(d) volume
(a) temperature

Question 8.
……………….consists of ‘U’ shape metal frame
(a) Screw gauge
(b) Vernier caliper
(c) Beam balance
(d) Spring balance
(a) screw gauge

Question 9.
Least count of a vernier caliper is ……………. cm.
(a) 1
(b) 0.1
C) 0.01
(d) 0.001
(c) 0.01

Question 10.
If no object is placed on the hook, then the pointer of the spring balance reads ………………….
(a) 3
(b) 2
(c) 1
(d) 0
(d) 0

Question 11.
SI unit of mass and weights are ………………….
(a) kg, N
(b) N, kg
(c) K, N
(d) N, K
(a) kg, N

Question 12.
Units named after scientists …………………..
(a) lowercase
(b) upper case
(c) both (a) and (b)
(d) neither (a) or (b)
(a) lower case

Question 13.
An instrument that is used to measure the diameter of a cricket ball is ………………….
(a) Screw gauge
(b) Meter scale
(c) Vernier caliper .
(d) Spring balance
(a) Vernier caliper

Question 14.
Distance between Chennai and Kanyakumari can be found in
(a) Kilometres
(b) Metres
(c) Centimetres
(d) Millimetres.
(a) Kilometres

II. Fill in the blanks :

1. The precision of vernier calipers is ……………. mm.
(a) 0.1mm

2. The gravity accelerates an object, the distance fallen is proportional to …………………
time squared

3. SI unit of electric current is ………………
ampere

4. Larger unit for measuring time is ………………..
millennium

5. The value of an astronomical unit is ……………………
1.496 x 1011

6. Mass is a …………….. quantity.
scalar

III. State whether true or false. If false, correct the statement:

1. The precision of screw gauge is 0.001 cm.
True.

2. The unit of amount of substance is candela
False.
Correct statement: The unit of amount of substance is mole.

3. The symbol for the units derived from the names of scientists are written in capital letter
True.

4. Yard was used as the unit of length.
True

5. Micron is also known as micro-metre
True

6. A vemier caliper using the scale invented by Galileo.
False.
Correct statement: A vernier caliper using the scale invented by Pierre Vernier.

7. The SI unit of mass is kg.
True.

8. Weight has both magnitude and direction.
True.

IV. Match the following:

Question 1.

 Column I Column II FPS Metre, kilogram and second CGS Foot, pound and second MKS or SI centimetre, gram and second

 Column I Column II FPS Foot, pound and second CGS centimetre, gram and second MKS or SI Metre, kilogram and second

Question 2.

 Column-I Column-II 10 years 1 year 10 centuries 1century(100 years) 10 decades 1 millennium 365.24 days 1 decade

 Column-I Column-II 10 years 1 decade 10 centuries 1 millennium 10 decade 1century(100 years) 365.24 days 1 year

Question 3.

 Column-I Column-II Electric Current radian Luminous intensity ampere Angle steradian Solid angle candela

 Column-I Column-II Electric Current ampere Luminous intensity candela Angle radian Solid angle steradian

Question 4.

 Column-I Column-II Length s Mass m Time k Temperature kg

 Column-I Column-II Length m Mass kg Time s Temperature k

Question 5.

 Column-I Column-II Millimeter 10-15 m Nanometer 10-3m Angstrom 10-9m Fermi 10-10m

 Column-I Column-II Millimeter 10-3m Nanometer 10-9m Angstrom 10-10m Fermi 10-15 m

Question 6.

 Column-I Column-II Temperature Bearm balance Mass Ruler Length Digital clock Time Thermometer

 Column-I Column-II Temperature Thermometer Mass Bearm balance Length Ruler Time Digital clock

V. Assertion and reason type :

Question 1.
Assertion (A) : Light year and wave length both measure distance
Reason (R) : Both have dimensions of time.
(a) Both A and R are true but R is not the correct explanation of A.
(b) Both A and R are true and R is the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
(c) A is true but R is false

Question 2.
Assertion (A) : Density is a derived physical quantity
Reason (R) : Density cannot be derived from the fundamental physical quantities.
(a) Both A and R are true but R is not the correct explanation of A.
(b) Both A and R are true and,R-is the correct explanation of A.
(c) A is true but R is false. .
(d) A is false but R is true.
(c) A is true but R is false
Correct statement: Density can be derived from mass and volume.

Question 3.
Assertion (A) : Mass, Length and Time are fundamental physical quantities.
Reason (R) : They are independent of each other.
(a) Both A and R are true but R is not the correct explanation of A.
(b) Both A and R are true and R is the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
b) Both A and R are true and R is the correct explanation of A

Question 4.
Assertion (A) : The SI system of units is the improved system of units for measurement.
Reason (R) : The SI unit of mass is kilogram.
(a) Both A and R are true but R is not the correct reason.
(b) Both A and R are true and R is the correct reason.
(c) A is true but R is false.
(d) A is false but R is true.
(b) Both A and R are true and R is the correct reason

Question 5.
Assertion (A) : The skill of estimation is important for all of us in our daily life.
Reason (R) : The skill of estimation reduces our consumption of time.
a) Both A and R are true but R is not the correct reason.
b) Both A and R are true and R is the correct reason.
c) A is true but R is false. ,
d) A is false but R is true.
(b) Both A and R are true and R is the correct reason

VI. Comprehensive type :

(a) The speed of a body gives us an idea of how slow or fast that a body is moving. Speed of a body is the distance travelled by it per unit time. The SI unit of speed is metre per second. It is a scalar quantity. The speed of a running cab at any instant of time is shown by an instrument called, ’speedometer’ and the distance travelled by a car is measured by another instrument called, ‘odometer’.

Question 1.
Which the following is not a correct unit of speed?
(a) cm/s
(b) m/s
(e) km/h
(d) km/s.
(d) km/s

Question 2.
If the distance travelled by the cab in 3 hours is 120 km, then its speed will be
(a) 40 m/s
(b) 40 km/s
(c) 40 km/h
(d) 40 km/min
(c) 40 km/h

Question 3.
The formula for finding the speed of the cab is
(a) Distance = speed x time
(b) velocity = distance x time
(c) time = distance x velocity
(d) None of these.
(a) Distance = speed x time

Mass is the amount of matter contained in an object. Measurement of mass helps us to distinguish between lighter and a heavier body. Beam-Balance, spring balance and electronic balance are used to measure mass of different objects. The SI unit of mass is kilogram (kg). But different units are Used to measure the mass of different objects depending upon their weight, e.g. weight (mass) of a tablet is measured in milligrams (mg), weight of a student is measured in kilogram (kg), and weight of a truck with goods is measured in metric tons. 1 metric ton is equal to 10 quintals and 1 quintal is equal to 100 kg. 1 gram is equal to 1000 mg.

Question 1.
The value of 1 metric ton is equal to
(a) 1000 kg
(b) 10 quintals
(c) 1000,000 g
(d) 100 kg
(a) 1000 kg (or) (b) 10 quintals

Question 2.
How will you measure weight of a tablet?
(a) kg
(b) g
(c) mg
(d) none of these.
(c) mg

Question 1.
Write the units which are used to measure long distances.
km, AU, light-year, parsec.

Question 2.
Define Astronomical unit.
AU is defined as the average distance between the earth and the sun.
1 AU = 1.496 × 1011m.

Question 3.
Define the light year.
The distance travelled by light in one year in vacuum. 1 light-year = 9.46 × 1015m.

Question 4.
Convert the temperature from Fahrenheit into Celsius & Kelvin.

Question 5.
Convert 100°C into Kelvin.
100 + 273 = 373 K. ie. °C + 273

Question 6.
Convert 112°F into K.

Question 7.
Write the principle of screw gauge.

• When a screw is rotated in a nut, the distance moved by the tip of the screw is directly proportional to the number of rotations given.
• Hence the principle of the screw is considered as the principle of screw gauge.

Question 8.
What are the kinds of units?

1. Fundamental or basic units
2. Derived units

Question 9.
Give some examples of fundamental units.
The examples of fundamental units are kg for mass,m for length, s for time.

Question 10.
Give some examples of derived units.
The units of area, volume, density.

Question 11.
What is the standard unit of weight?
Newton is the standard unit of weight.

Question 12.
What is the standard unit of mass?
kilogram is the standard unit of mass.

Question 13.
Define Mass.
Mass is the amount of matter contained in a body.

Question 14.
Define Weight.
The force with which the earth attracts a body towards its center is called weight.

Question 15.
What is the SI unit of temperature?
Kelvin is the SI unit of temperature.

Question 16.
What is the measuring unit of the thickness of a plastic carry bag?
1 micron = 10-6m (or) μm.

Question 1.
Write temperature conversion.
Temperature Conversion (Exact)

Question 2.
Write about the positive zero error in screw gauge instrument.
When the plane surface of the screw and the opposite plane stud on the frame are brought into contact, if the zero of the head scale lies below the pitch scale axis, the zero error is positive. For example, the 5th division of the head scale coincides with the pitch scale axis, then the zero error is positive and is given by Z.E = + (n × LC) where ‘n’ is the head scale coincidence. In this case, Zero error = + (5 × 0.01) = 0.05 mm. So the zero correction is – 0.05 mm

Question 3.
Write SI units for the fundamental quantity.

 Basic Quantity Unit Length metre Mass kilogram Time second Electric current ampere Temperature kelvìn Amount of substance mole Luminous intensity candela

Question 4.
Convert the following units in metre.

 Smaller units Value in metre Centimeter (cm) 10-2 m Millimeter (mm) 10-3 m micron or µm 10-6 m nanometre (nm) 10-9 m angstrom (A) 10-10 m fermi (f) 10-15 m

Question 5.
Draw and mark the parts of vernier caliper
PARTS Marked in the Vernier caliper

1. Lower fixed jaw
2. Upper fixed jaw
3. Lower movable jaw
4. Vernier scale
5. Retainer
6. Main scale
7. Depth probe.

IX. Numerical Problems :

Question 1.
A piece of iron of volume 40cm3 whose density is 6.8g/cm3. Find the mass of iron.
Given, density of iron, D = 6.8g/cm3
volume of iron, V = 40 cm3
mass of iron, M = V × D [∴ mass = volume × density]

m = 272.0g.

Question 2.
Solve : The mass of 40 apples in a box is 5 kg.
(i) Find the mass of a dozen of them.
(ii) Express the mass of one apple in gram.
(i)  40 apple = 5 kg 5000 g
1 apple =$$\frac{500 \not 0}{4 \not \emptyset}$$
1 apple 125 g
∴ 1 dozen 12 apples
12 apples 125 × 12 g
12 apples 1500 g.

(ii)  40 apples = 5000 g

1 apple = $$\frac{5000}{40} \mathrm{~g}$$

1 apple = 125 g
The mass of 1 apple = 125 g

Question 1.
How will you find Zero Error of the screw gauge?
Zero Error of a screw gauge :
When the plane surface of the screw and the opposite plane stud on the frame area brought into contact, if the zero of the head scale coincides with the pitch scale axis there is no zero error.

Positive zero error:
When the plane surface of the screw and the opposite plane stud on the frame are brought into contact, if the zero of the head scale lies below the pitch scale axis, the zero error is positive. For example, the 5th division of the head scale coincides with the pitch scale axis, then the zero error is positive and is given by
Z.E = + (n x LC) where ‘n’ is the head scale coincidence. In this case, Zero error = + (5 x 0.01) = 0.05mm. So the zero correction is -0.05 mm.

Negative zero error:
When the plane surface of the screw and the opposite plane stud on the frame are brought into contact, if the zero of the head scale lies above the pitch scale axis, the zero error is negative. For example, the 95th division coincides with the pitch scale axis, then the zero error is negative and is given by
ZE = -(100-n) × LC
ZE = – (100 – 95) × LC
= -(5 × 0.01)
= – 0.05 mm
The zero correction is + 0.05mm

Question 2.
How will you find Zero Error of Vernier Caliper? Explain.
Zero error:

• Unscrew the slider and move it to the left, such that both the jaws touch each other. Check whether the zero marking of the main scale coincides with that of the Vernier scale.
• If they are not coinciding with each other, the instrument is said to posses zero error. Zero error may be positive or negative.
• If the zero mark of the Vernier is shifted to the right, it is called positive error.
• On the other hand, if the Vernier zero is shifted to the left of the main scale zero marking, then the error is negative.

Positive zero error:

• From the figure you can see that zero of the vernier scale is shifted to the right of zero of the main scale.
• In this case the reading will be more than the actual reading.
• Hence, this error should be corrected. In order to correct this error, find out which vernier division is coinciding with any of the main scale divisions.
• Here, fifth vernier division is coinciding with a main scale division.
• So, positive zero error = +5 × LC = +5 × 0.01 = 0.05 cm.

Negative zero error:

• You can see that zero of the vernier scale is shifted to the left of the zero of the main scale.
• So, the obtained reading will be less than the actual reading.
• To correct this error we should first find which vernier division is coinciding with any of the main scale divisions, as we found in the previous case.
• In this case, you can see that sixth line is coinciding. But, to find the negative error, we can count backward (from 10).
• So, the 4th line is coinciding. Therefore, negative zero error = -4 x LC = -4 x 0.01 = -0.04 cm.

Question 3.
Write short note on the following :
(i) Common balance
(ii) Physical balance Digital balance Spring balance
Common (beam) balance :
A beam balance compares the sample mass with a standard reference mass (Standard reference masses are 5g, 10g, 20g, 50g, 100g, 200g, 500g, 1kg, 2kg, 5kg). This balance can measure mass accurately up to 5 g

Physical balance:
This balance is used in labs and is similar to the beam balance but it is a lot more sensitive and can measure mass of an object correct to a milligram.
The standard, reference masses used in this physical balance are 10 mg, 20 mg, 50 mg, 100 mg, 200 mg, 500 mg, 1 g, 2g, 5 g, 10 g, 20 g, 50 g, 100g, and 200 g.

Digital balance:
Nowadays, for accurate measurements digital balances are used, which measure mass accurately even up to a few milligrams, the least value being 10 mg (Figure 1.11). This electrical device is easy to handle and commonly used in jewellery shops and labs.

Spring balance:
This balance helps us to find the weight of an object. It consists of a spring fixed at one end and a hook attached to a rod at the other end. It works by ‘Hooke’s law’ which states that the addition of weight produces a proportional increase in the length of the spring. A pointer is attached to the rod which slides over a graduated scale on the right. The spring extends according to the weight attached to the hook and the pointer reads the weight of the object on the scale.

## Samacheer Kalvi 9th Science Guide Chapter 7 Heat

Tamilnadu State Board New Syllabus Samacheer Kalvi 9th Science Guide Pdf Chapter 7 Heat Text Book Back Questions and Answers, Notes.

## Tamilnadu Samacheer Kalvi 9th Science Solutions Chapter 7 Heat

### 9th Science Guide Heat Text Book Back Questions and Answers

I. Choose the correct answer :

Question 1.
Calorie is the unit of
(a) heat
(b) work
(c) temperature
(d) food
(a) heat

Question 2.
SI unit of temperature is
(a) fahrenheit
(b) joule
(c) Celsius
(d) kelvin
(d) kelvin

Question 3.
Two cylindrical rods of same length have the area of cross section in the ratio 2:1. If both the rods are made up of same material, which of them conduct heat faster?
(a) Both rods
(b) Rod-2
(c) Rod-1
(d) None of them
(c) Rod-1

Question 4.
In which mode of transfer of heat, molecules pass on heat energy to neighbouring molecules without actually moving from their positions?
(b) Conduction
(c) Convection
(d) Both B and C

Question 5.
A device in which the loss of heat due to conduction, convection and radiation is minimized is
(a) Solar cell
(b) Solar cooker
(c) Thermometer

II. Fill in the blanks:

1. The fastest mode of heat transfer is ……………………….

2. During day time, air blows from ……………………… to………………………
sea to land

3. Liquids and gases are generally ……………………… conductors of heat.
poor

4. The fixed temperature at which matter changes state from solid to liquid is called………………………
melting point

III. Assertion and Reason type questions :

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

Question 1.
Assertion : Food can be cooked faster in vessels with copper bottom.
Reason : Copper is the best conductor of heat.
(a) Both assertion and reason are true and reason is the correct explanation of assertion

Question 2.
Assertion : Maximum sunlight reaches earth’s surface during the noon time.
Reason : Heat from the sun reaches earth’s surface by radiation.
(b) Both assertion and reason are true but the reason is not the correct explanation of the assertion
Reason : When the sun is at its highest point, the earth’s surface absorbs more heat and retains. This heat is slowly radiated out causing increase in temperature.

Question 3.
Assertion : When water is heated up to 100° C, there is no raise in temperature until all water gets converted into water vapour.
Reason : Boiling point of water is 10° C.
(c) Assertion is true but the reason is false
Reason : When a substance changes from one state to another, a considerable amount of heat energy is absorbed or liberated. This energy is called latent heat.

Question 1.
Define conduction.
The process of transfer of heat in solids from a region of higher temperature to a region of lower temperature without the actual movement of molecules is called conduction.

Question 2.
Ice is kept in a double-walled container. Why?
An ice-box is made of double wall and the space between the walls is filled with some non-conducting materials to provide heat insulation, so that the loss of heat can be minimized. Hence ice is kept in a double-walled container.

Question 3.
How does the water kept in an earthen pot remain cool?
An earthen pot consists of small pores from which the water inside the pot constantly seeps out and gets evaporated due to the presence of high temperatures around it. The evaporation process requires heat which is acquired from the surface of the pot, hence making the water and the pot cooler.

Question 4.
Convection

1. The process of transfer of heat in which the heated molecules of a liquid (or gas) themselves move to carry heat from the hot to the cold end is called convection.
2. Ex : Land and sea breeze.
3. Convection need matter to be present.

1. The process of transfer of heat in which a material medium is not necessary and heat is directly transferred from the hot body to the cold body is called radiation.
2. Ex : Transfer of heat energy from the sun.
3. Radiation can occur even in a vacuum.

Question 5.
Why do people prefer wearing white clothes during summer?
People prefer white or light coloured clothes during summer as they are good reflectors of heat and hence, they keep us cool.

Question 6.
What is specific heat capacity?
Specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of 1 kg of the substance by 1°C or 1 K.

Specific Heat Calculator is a free online tool that displays the amount of heat per unit mass.

Question 7.
Define thermal capacity.

• Heat capacity or thermal capacity is defined as the amount of heat energy required to raise the temperature of a body by 1°C. It is denoted by ‘C’.
• C = Q/t, where C’ is the heat capacity, ‘Q’ is the quantity of heat required and ‘f’ is rise in temperature.
• SI unit of heat capacity is J/K. It is also expressed in cal/°C, kcal/°C or J/°C.

Question 8.
Define specific latent heat capacity.
Specific latent heat is the amount of heat energy absorbed or liberated by unit mass of a substance during change of state without causing any change in temperature.

Question 1.
Explain convection in daily life.
Convection is the flow of heat through a fluid from places of higher temperature to places of lower temperature by movement of the fluid itself.

Hot air balloons:
Air molecules at the bottom of the balloon get heated by a heat source and rise. As the warm air rises, cold air is pushed downward and it is also heated. When the hot air is trapped inside the balloon, it rises.

Breeze :
During day time, the air in contact with the land becomes hot and rises. Now the cool air over the surface of the sea replaces it. It is called sea breeze. During night time, air above the sea is warmer. As the warmer air over the surface of the sea rises, cooler air above the land moves towards the sea. It is called land breeze.

Chimneys :
Tall chimneys are kept in kitchen and industrial furnaces. As the hot gases and smoke are lighter, they rise up in the atmosphere.

Question 2.
What are the changes of state in water? Explain.

• The process of changing of a substance from one physical state to another at a definite temperature is defined as change of state.
• For example, water molecules are in liquid state at normal temperature.
• When water is heated to 100°C, it becomes steam which is a gaseous state of matter. On reducing the temperature of the steam it becomes water again.
• If we reduce the temperature further to 0°C, it becomes ice which is a solid state of water. Ice on heating, becomes water again.
• Thus, water changes its state when there is a change in temperature.
• The process in which a solid is converted to liquid by absorbing heat is called melting or fusion.
• The process in which a liquid is converted to solid by releasing heat is called freezing.
• The process in which a liquid is converted to vapor by absorbing heat is called boiling or vaporization.
• The process in which a vapour is converted to liquid by releasing heat is called condensation.
• The process in which a solid is converted to gaseous state is called sublimation.

Question 3.
How can you experimentally prove water is a bad conductor of heat? How is it possible to heat water easily while cooking?
(a) Half fill a test tube with cold water. Wrap a piece of ice in wire gauze and drop it in the tube.
(i) It will sink to the bottom.
(ii) Now heat the top end of the test tube.
(iii) The water soon begins to boil at the top but the ice below has still not fully melted.

This activity shows that water is a bad conductor of heat. It does not easily conduct heat from the top to the bottom of the test tube.

(b) It is possible to heat water easily while cooking:

• ill a test tube with cold water.
• Drop an ice-cube in this water.
• Now heat the water from below.
• You will find that the ice melts quickly.
This shows that though water is a bad conductor of heat, heat easily flows upwards in it. This method of transfer of heat is called convection. This method is involved in cooking.

VI. Numerical Problems.

Question 1.
What is the heat in joules required to raise the temperature of 25 grams of water from 0°C to 100°C? What is the heat in Calories? (Specific heat of water = 4.18 J/g°C)
Given : Mass of water m = 25g
Initial temperature T1 = 0°C
Final temperature T1 = 100°C
Change in temperature ΔT = (T2 – T1)
= (100 – 0)°C [ΔT= 100°C]
Specific heat of water C = 4.18 J/g°C
Solution:
The heat required H (in joules) = m × c × ΔT
= 25 × 4.18 × 100
= 25 × 418
= 10450 J
Heat required in calories = 1 calorie = 4.18 J
10450 J = 2497.60 calories

Question 2.
What could be the final temperature of a mixture of 100 g of water at 90°C and 600 g of water at 20°C.
Mass of water m1 = 100 g = 0.1 kg
Specific heat capacity of water c = 4186 J
Temperature = 90°C
Mass of water m2 = 600 g = 0.6 kg
Temperature = 20°C
Solution:
Heat lost by hot water = Heat gained by cold water
m1 × c × θ1 = m2 × c × θ2
0.1 × 4186 x (90 – TF) = 0.6 × 4186 × (TF – 20)
0.1 × (90 – TF) = (TF – 20) × 0.6
9 – 0.1 TF = 0.6TF – 12
0.7TF = 21
TF = 30°C
Final temperature of a mixture = 30°C

Question 3.
How much heat energy is required to change 2 kg of ice at 0°C into water at 20°C? (Specific latent heat of fusion of water = 3,34,000J/kg, Specific heat capacity of water = 420OJKg-1K-1
Solution:
Mass of ice m = 2 kg
Specific latent heat of fusion of water = L = 3, 34, 000 J/kg
Change in temperature ΔT = (T2 – T1)
= (20 – 0)° C
ΔT = 20° C
Specific heat capacity of water C = 4200 J Kg-1K-1
Heat energy required= m × c × ΔT + m × L
= 2 × 4,200 × 20 + 2 × 3,34,000
= 1,68,000 + 6,68,000
Heat Energy required = 8,36,000 J

Intext Activities

ACTIVITY – 1

Take a glass of water and put some ice cubes into it. Observe it for some time. What happens? The ice cubes melt and disappear. Why did it happen? It is because heat energy in the water is transferred to the ice.

Aim:
To demonstrate transfer of heat.

Material required :
A glass of water, ice cubes.

Procedure:
Take a glass of water and put some ice cubes into it. Observe it for some time. What happens?

Observation :
The ice cubes melt and disappear. It is because heat energy in the water is transferred to the ice.

Conclusion :
Heat transfer takes place when heat energy flows from the object of higher temperature to an object with lower temperature.
[End of the activity]

ACTIVITY – 2

Take metal rods of copper, aluminum, brass and iron. Fix a match stick to one end of each rod using a little melted wax. When the temperature of the far ends reach the melting point of wax, the matches drop off. It’s observed that the match stick on the copper rod would fall first, showing copper as the best conductor followed by aluminum, brass and iron.

Aim :
To compare the conducting powers of various metals.

Materials required :
Metal roads of copper, aluminium, brass and iron, match stick, melted wax.

Procedure :
Fix a match stick to one end of each rod using the little melted wax. When the temperature of the far ends reach the melting point of wax, the matches drop. Observe what happens?

Observation :
The match stick on the copper rod would fall first, showing copper as the best conductor followed by aluminum, brass and then iron.

Conclusion:
Metals are good conductors of heat. Copper is the best conductor of heat.
[End of the activity]

ACTIVITY – 3

Drop a few crystals of potassium permanganate down to the bottom of a beaker containing water. When the beaker is heated just below the crystals, by a small flame, purple streaks of water rise upwards and fan outwards.

Aim :
To demonstrate transfer of heat through convection in liquids.

Materials required :
Crystals of potassium permanganate, beaker containing water.

Procedure :
Drop a few crystals of potassium permanganate down to the bottom of a beaker containing water, heat it with a small flame.

Observation :
When the beaker is heated, just below the crystals purple streaks of water rise upwards and fan outward.

Conclusion :
Water molecules at the bottom of the beaker receive heat energy and move upward and replace the molecules at the top.
This activity shows that the flow of heat through a fluid from places of higher temperature to places of lower temperature by movement of the fluid itself.
[End of the activity]

ACTIVITY – 4

Take some crushed ice cubes in a beaker and note down the temperature using thermometer. It will be 0°C. Now heat the ice in the beaker. You can observe that ice is melting to form water. Record the temperature at regular intervals and it will remain at 0°C until whole ice is converted to liquid. Now heat the beaker again and record the temperature. You can notice that the temperature will rise up to 100°C and it will retain the same even after continuous heating until the whole mass of water in the beaker is vaporized.

Aim :
To understand latent heat of the water.

Materials Required :
Crushed ice cubes, beaker and thermometer.

Procedure :
Take some crushed ice cubes in a beaker and note down the temperature using thermometer. It will be 0°C. Now heat the ice in the beaker, (i) Observe and record the temperature at regular intervals. Heat the beaker again and record the temperature.

Observation :

• Ice is melting to form water.
• Water will remain at 0°C until the whole ice is converted to liquid.
• On further heating, we can observe that the temperature will rise up to 100°C and the temperature will be at 100°C even after continuous heating until the whole mass of water in the beaker is vapourized.

Conclusion :
In this activity, the temperature is constant at 0°C until entire ice is converted into liquid and again constant at 100°C until all the water is converted into vapour.
It is because, when a substance changes from one state to another, a considerable amount of heat energy is absorbed or liberated. This energy is called latent heat.

Question 1.
Water is used as a coolant because it ………………….
(a) is inexpensive
(b) is easily available
(c) is a good conductor of heat
(d) has a high specific heat capacity
(d) has a high specific heat capacity

Question 2.
The amount of heat required to raise the temperature through 1°C is called………………………
(a) thermal energy
(b) calorie
(c) heat capacity
(d) specific heat capacity
(c) heat capacity

Question 3.
The temperature at which a liquid gets converted into its vapour state is called its………………………
(a) melting point
(b) boiling point
(c) dew point
(d) freezing point
(b) boiling point

Question 4.
Sweating causes cooling because water has a………………………
(a) high specific heat
(b) low specific heat
(c) high latent heat of fusion
(d) high latent heat of vaporisation
(d) high latent heat of vaporisation

Question 5.
Which of the following is true?
(a) 1 J = 412 calorie
(b) 1 J = 0.24 calorie
(c) 1 calorie = 4.2 J
(d) Both b and c
(c) 1 calorie = 4.2 J

Question 6.
Ice does not melt rapidly because of
(a) high specific heat capacity
(b) high latent of fusion
(c) high heat capacity
(d) high latent heat of fusion
(d) high latent heat of fusion

Question 7.
Which one of the following scales has a lower fixed point at 0°C?
(a) Kelvin scale
(b) Fahrenheit scale
(c) Celsius scale
(d) All of these
(c) Celsius scale

Question 8.
When we heat one end of an iron rod, its other end also gets heated. Can you say, Which one of the following is behind this?
(a) Convection of heat
(c) Insulation of heat
(d) Conduction of heat
(d) Conduction of heat

Question 9.
In which of the following, chemical energy is converted into heat energy?
(a) Heater
(b) Refrigerators
(c) Candle
(d) Motor
(c) Candle

Question 10.
On a cold day, it is hard to open the lid of a tight container. But when you gently heat the neck you can easily open the lid. why?
(a) On heating glass expands and lid contracts
(b) On heating lid expands more than the neck and thus slides easily
(c) Neck becomes slippery on heating
(d) Lid of the bottle cannot bear the heat.
(b) On heating lid expands more than the neck and thus slides easily

Question 11.
Warm air is ………………………
(a) lighter than cold air
(b) heavier than cold air
(c) both have equal weights
(d) cannot be said
(a) lighter than cold air

Question 12.
The phenomenon involved in the sea breeze and the land breeze is ………………………
(a) convection
(b) conduction
(d) none of these
(a) convection

Question 13.
A liquid changes into a gas at a constant temperature known as its………………………
(a) absolute zero
(b) boiling point
(c) evaporation point
(d) dew point
(b) boiling point

Question 14.
Copper and Iron are good conductors of heat. Which one of the following is not a good conductor of heat?
(a) Soil
(b) Aluminium
(c) Tungsten
(d) Steel
(a) Soil

Question 15.
The specific heat capacity of water is
(a) 4200 Jkg-1K-1
(b) 420 Jg-1K-1
(c) 0.42 Jg-1K-1
(d) 4.2 Jkg-1K-1
(a) 4200 Jkg-1K-1

Question 16.
Two cylinders of equal height and radius are made of copper and aluminum. Which of them conducts heat faster?
(a) Copper rod
(b) Aluminium rod
(c) Both of them
(d) None of them
(a) Copper rod

II. Fill in the blanks:

1. ………………………is a process which is just reverse of melting.
Freezing

2. While a substance is undergoing a change of state, the temperature of the body remains ………………………
same

3. A change of state is a change of a substance from………………………
one physical state to another

4. ………………………is the degree of hotness or coldness of a body.
Temperature

5. The solid, liquid, gaseous phases of water can coexist in equilibrium at………………………
273.16K

6. The sum of the kinetic and potential energy is called the ………………………of the molecules.
internal energy

7. ……………………… is greater for liquids than that for solids and maximum in case of gases.
Expansion

8. When heat energy is added to a substance, the kinetic energy of its particles and so the particles ……………………… move at a higher speed.
increase

9. When a dog keeps out its tongue and breathes hard, the moisture on the tongue turns into ………………………and it evaporates.
water

10. Black marks appearing on the ceiling above a lamp or fan caused by dust being carried upwards in the air are due to………………………
convection currents

11. ………………………is the method of heat transfer that does not require particles to carry the heat energy.

12. Radiation consists of ………………………waves travelling at the speed of light.
electromagnetic

13. We can observe all the three ways of heat transfer while………………………
burning wood

14. ……………………… is known as an absolute scale.
Kelvin

15. Specific latent heat L =………………………
Q/m

III. Match the following :

 Column A Column B 1. Heat a) Heat gained or lost in the change of state with out any change in temperature 2. m × L. b) Heat gained or lost when there is no change of state 3. Temperature c) Form of energy 4. m × s × t d) SI unit of specific latent heat 5. J/Kg e) degree of hotness or coldness

1-c, 2 -a, 3 — e, 4-b, 5-d

II.

 Column A Column B 1. Specific heat capacity of water a) 0°C 2. Latent heat of fusion of ice b) 2260 J/g 3. Latent heat of vaporisation of water c) 100°C 4. Melting point of ice d) 4.2 J/g°C 5. Boiling point of water e) 336 J/g

1-d, 2 -e, 3 – b, 4-a, 5-c

IV. Assertion and Reason type questions :

Question 1.
Assertion (A) : Temperature is the measure of heat energy.
Reason (R) : Energy is the capacity to do work.
(a) If both assertion and reason are true and the reason is the correct explanation of assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of assertion.
(c) If assertion is true but reason is false.
(d) If assertion is false but reason is true.
(b) Both assertion and reason are true but the reason is not the correct explanation of the assertion
Reason: It is the degree of hotness or coldness of a body.

Question 2.
Assertion (A): Radiation is a process of transfer of heat in which a material medium is not necessary.
Reason (R): The heat from the sun reaches us through millions of miles of empty space by convection.
(a) If both assertion and reason are true and reason is the correct explanation of assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of assertion.
(c) If assertion is true but reason is false.
(d) If assertion is false but reason is true.
(c) Assertion is true but reason is false
Reason : All hot bodies radiate’ heat, therefore from the sun the heat comes to us by radiation.

Question 3.
Assertion (A) : Heat energy is transferred from one body to another due to a
temperature difference between them.
Reason (R) : Heating a substance causes a rise in temperature.
(a) If both assertion and reason are true and reason is the correct explanation of assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of assertion.
(c) If assertion is true but reason is false.
(d) If assertion is false but reason is true.
(b) Both assertion and reason are true but reason is not the correct explanation of assertion
Reason : Heat energy is more in hot substances and less in cold substances and flows from hot substances to cold substances.

Question 4.
Assertion (A) : When a very hot liquid is poured into a thick glass tumbler it cracks.
Reason (R) : Unequal expansion of the inner and outer glass walls causes the glass to crack.
(a) If both assertion and reason are true and reason is the correct explanation of assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of assertion.
(c) If assertion is true but reason is false.
(d) If assertion is false but reason is true.
(a) Both assertion and reason are true and reason is the correct explanation of assertion

V. Very short answer type questions.

Question 1.
What is the other name of heat capacity?
Thermal capacity.

Question 2.
Define one calorie.
The amount of heat energy required to raise the temperature of 1 g water by 1°C is called one calorie.

Question 3.
What is the relation between calorie and Joule?
1 Calorie = 4.186 J
= 4.2 J

Question 4.
Name a device that prevents loss of energy (or gain) by conduction, convection and radiation.

Question 5.
Which factor determines the direction of flow of heat from one body to another?
Temperature.

Question 6.
Who introduced the term latent heat?
Joseph Black in 1750.

Question 7.
What is the minimum possible temperature? Is there also a maximum possible temperature?
The minimum possible temperature is OK. There is no limit to maximum temperature.

Question 1.
Heat gained by a body depends upon which factors?

• Mass of the body
• Change in temperature of the body
• Nature of the material of the body.

Question 2.
Water is used as a coolant in car radiators. Why?
Water is used as a coolant in car radiators because it has high specific heat capacity. As a result, it can absorb large amounts of heat from the car engine without any substantial increase in its temperature.

Question 3.
What do you mean by thermal equilibrium?
When two bodies at different temperatures are kept in contact with each other, then heat energy flows from the hot body to the colder one.

It means that the hot body will lose heat and the cold body will gain heat till they reach a common temperature. This state is called thermal equilibrium.

Question 4.
Define latent heat of fusion?
Heat energy is absorbed by a solid during melting and an equal amount of heat energy ‘ is liberated by the liquid during freezing, without any temperature change. It is called latent heat of fusion.

Question 5.
Why are burns caused by steam more painful than those caused by boiling water at the same temperature?

• When steam hits our skin, it condenses to water and then cools down to the temperature of skin.
• Now, the energy released will be due to latent heat and fall in temperature.
• Whereas when boiling water hits our skin, there is no phase transition but only fall in temperature and the heat transferred to skin will be only due to cooling.
• Also, the loss of energy that is released from steam hitting our skin occurs quickly and in a small localized area, therefore causing damage to our cells.

Question 6.
What do you mean by solidification or deposition?
Solidification is the process in which a gas directly condenses into its solid state without going into liquid state Ex : Carbon dioxide gas gets converted into dry ice.

Question 7.
Define absolute zero.
The temperature at which the pressure and volume of a gas theoretically reaches zero is called absolute zero.

Question 8.
Give some practical applications of conduction in daily life.

• Metals are good conductors of heat. So, aluminium is used for making utensils to cook food quickly.
• Mercury is used in thermometers because it is a good conductor of heat.
• We wear woolen clothes in winter to keep ourselves warm. Air, which is a bad conductor, does not allow our body heat to escape.

Question 9.
Give some practical applications of radiation.

• White or light colored clothes are good reflectors of heat. They keep us cool during summer.
• The bottom surface of cooking utensils is blackened because the black surface absorbs more heat from the surrounding.
• The surface of the airplane is highly polished because it helps to reflect most of the heat radiation from the sun.

Question 10.
Can convection take place in solids? Why?
No. The molecules in a solid are only free to vibrate about their fixed positions. For convection to take place, the molecules need to move to carry the heat with them. Hence, convection cannot take place in solids.

Question 11.
In winters, when the sun suddenly goes behind the clouds we feel cold, can you say why?
The clouds cut off the radiant heat from the sun.

Question 1.
Give the difference between heat and temperature.
Heat

1. Heat is a form of energy due to which we feel hot or cold.
2. Its SI unit is joule (J)
3. It depends upon mass, nature and temperature of the body.
4. It is a form of energy.
5. It is measured by a calorimeter.

Temperature :

1. The degree of hotness or coldness of a body is known as temperature.
2. Its SI unit is kelvin (K).
3. It does not depend upon mass, nature and temperature of the body.
4. It is a condition that determines the direction of flow of heat.
5. It is measured by a thermometer.

Question 2.
Give some practical applications of specific latent heat of ice.
Specific latent heat of ice is very high (i.e.) 336 J/g.

• Due to high specific latent heat of ice, snow on mountains do not melt as a whole, but melts gradually into water with the heat of the sun.
If the specific latent heat of ice would not have been so high, all the snow would have melted very quickly and there would have been floods in the rivers.
• All the water in lakes and ponds in cold places do not freeze all at the same time. If freezes slowly and keeps the surrounding moderate.
• Drinks are cooled more effectively by ice pieces at 0°C and not by water at 0°C. This is because 1 g of ice takes away 336 J of heat from the drink to melt into water at 0°C.

Question 3.
600 g of copper at 50°C is mixed with lOOOg water at 20°C. Find the final temperature of the mixture. Specific heat capacity of copper is 0.4 Jg-1°C-1 and that of water is 4.2 Jg-1°C-1
Solution :
Let final temperature of the mixture of copper and water = x °C
For copper:
Mass of copper m1 = 600g
Specific heat capacity of copper c1 = 0.4Jg-1°C-1
Initial temperature of copper t1 = 50°C
Final temperature of copper t2 = x°C
Fall in temperature Δt = (50 – x)°C
Heat lost by copper = m1 × c1 × t
= 600 × 0.4 × (50 – x)

For water :
Mass of water m2 = 1000g
Specific heat capacity of water c2 = 4.2Jg-1°C-14
Initial temperature of water t1 = 20°C
Final temperature of water t2 = x°C
Rise in temperature Δt = (x – 20)°C
Heat gained by water = m2 × c2 × t
= 100 × 4.2 × (x – 20)

According to the principle of calorimetry,
Heat lost by copper = Heat gained by water
600 × 0.4 × (50 – x) =1000 x 4.2 x (x – 20)
240 × (50 – x) = 4200 ( x- 20)
12,000 – 240x = 4200x-84000
4200x + 240x =12000 + 84000
4440 = 96000
x = $$\frac{96000}{4440}=21.6$$
So, final temperature of mixture of water and copper x = 21.6°C

Question 4.
Compare heat capacity and specific heat capacity.
Specific heat capacity :

1. It is the heat required to raise the temperature of 1g of a substance through 1°C.
2. It does not depend on the mass of the body It depends on the mass of the body
3. Its unit is Jkg-1 °C-1

Heat capacity

1. It is the heat required to raise the temperature of a given mass of substance through 1°C.
2. It depends on the mass of the body
3. Its unit is J°C-1.

Question 5.
Explain the following effects of heat.
(i) Expansion
(ii) Change in temperature
(iii) Change in state
(iv) Chemical changes.
(i) Expansion:
When heat is added to a substance, the molecules gain energy and vibrate and force other molecules apart. As a result, expansion takes place. You would have seen some space being left in railway tracks. It is because, during summer time, more heat causes expansion in tracks. Expansion is greater for liquids than for solids and maximum in case of gases.

(ii) Change in temperature :
When heat energy is added to a substance, the kinetic energy of its particles increases and so the particles move at higher speed. This causes rise in temperature. When a substance is cooled, that is, when heat is removed, the molecules lose heat and its temperature falls.

(iii) Change in state :
When you heat ice cubes, they become water and water on further heating changes into vapour. So, solid becomes liquid and liquid becomes gas, when heat is added. The reverse takes place when heat is removed.

(iv) Chemical changes :
Since heat is a form of energy it plays a major role in chemical changes. In some cases, chemical reactions need heat to begin and also heat determines the speed at which reactions occur. When we cook food, we light the wood and it catches fire and the food particles become soft because of the heat energy. These are all the chemical changes taking place due to heat.

VIII. Numerical Problems

Question 1.
What is the amount of heat required to raise the temperature of 5 kg of iron from 30°C to 130°C? Specific heat capacity of iron = 483 Jkg-1C-1.
Solution :
Mass of iron m = 5kg
Initial temperature t1 = 30°C
Final temperature t2 = 130°C
Rise is temperature Δt = (t2 -t1) = 130 – 30 = 100°C
Specific heat capacity of iron c = 483Jkg-1°C-1
Q = m × c × Δt
= 5 × 483 × 100
= 2,41,500J

Question 2.
Calculate the amount of heat required to convert 200g of ice at 0°C into the water at 0°C Specific latent heat of fusion of ice = 336 Jg-1
Solution :
Mass of ice m = 200g
Specific latent heat of fusion of ice L = 336Jg-1
Heat required Q = mL
= 200 × 336
Q = 67,200 J

Question 3.
2875 J of heat is required to melt 115 g of lead at its melting point. Calculate the specific latent heat capacity of fusion of lead.
Solution:
Mass of lead m = 115 g
Heat required Q = 2875 J
Specific latent heat of lead L =?
We know that Q = m L
L = $$\frac{Q}{m}=\frac{2875}{115}$$
= 25 Jg-1

Question 4.
What will be the final temperature if 1,68,000 J of heat is absorbed by 2 kg of water at 30°C?
Solution :
Heat absorbed Q = 1,68,000 J
m = 2kg
Initial temperature t1 = 30°C
Let final temperature t2 = x°C
Rise is temperature Δt = (t2 – t1)
= (x – 30)°C
Specific heat capacity of water C = 4200 J kg-1°C-1
We know that Q = m × c × Δt
1,68,000 = 2 × 4200 × (x – 30 )
x – 30 = $$\frac{1,68,000}{2 \times 4200}$$
x- 30 = 20
x = 30 + 20
= 50°C
So, the final temperature of water = 50°C

Question 5.
A metal ball of heat capacity 50J/°C loses 2000 J of heat. By how much will its temperature fall?
Solution :
Heat capacity of ball = 50 J °C-1
Heat lost Q = 200 J
Fall in temperature t =?

IX. Convert the following

1. 100°F to °C
Solution:
T(°C) = (T(°F) – 32) /1.8
T(°C) = (100°F – 32)
T(°C) = 37.7 °C

2. 40°C to Fahrenheit (°F)
Solution :
T(°F) = (T(°F) × 1.8) + 32
= 40°C × 1.8 + 32
= 72 + 32
T(°F) = 104°F

3. 35°C to Kelvin
Solution :
T(K) = T(°C) +273.15
= 35 + 273.15
T(K) = 308.15 K

4. 80°K to °C
Solution :
T(°C) = T(K) – 273.15
T(°C) = 80-273.15
T(°C) = 193.I5 °C

X. Define the following :

1. Heat: Heat is a form of energy which transfers from the higher temperature region to the lower temperature region of a body.
2. Conduction: The process of transfer of heat in solids from a region of higher temperature
to a region of lower temperature without the actual movement of molecules is called conduction.
3. Convection: Convection is the flow of heat through fluid from places of higher temperature to places of lower temperature by the movement of the fluid itself.
4. Radiation: Radiation is a method of heat transfer that does not require particles to carry the heat energy.
5. Temperature: Temperature is the degree of hotness or coolness of a body.
6. Specific heat capacity: Specific heat capacity of a substance is defined as the amount of heat required to raise the temperature of 1 kg of the substance by 1° C or 1 K.
7. Heat capacity or thermal capacity: Heat capacity is the heat required to raise the temperature of the entire mass of the body by 1° C.
8. Change of state: The process of changing of a substance from one physical state to another at a definite temperature is known as change of state.
9. Melting or fusion: The process in which a solid is converted to a liquid by absorbing heat is called melting or fusion.
10. Boiling: Th e process in which a liquid is converted to vapor by absorbing heat is called boiling or vaporization.
11. Sublimation: Th e process in which a solid is converted to a gaseous state is called sublimation.
12. Latent heat: Thus, latent heat is the amount of heat energy absorbed or released by a substance during a change in its physical states without any change in its temperature.
13. Specific latent heat: Specific latent heat is the amount of heat energy absorbed or liberated by the unit mass of a substance during a change of state without causing any change in temperature.

## Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Ex 8.1

Students can download Maths Chapter 8 Statistics Ex 8.1 Questions and Answers, Notes, Samacheer Kalvi 9th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 8 Statistics Ex 8.1

Question 1.
In a week, temperature of a certain place is measured during winter are as follows 26°C, 24°C, 28°C, 31°C, 30°C, 26°C, 24°C. Find the mean temperature of the week.
Solution:
Mean temperature of the week

= 27°C
Mean temperature of the week 27° C

Question 2.
The mean weight of 4 members of a family is 60 kg. Three of them have the weight 56 kg, 68 kg and 72 kg respectively. Find the weight of the fourth member.
Solution:
Weight of 4 members = 4 × 60 kg
= 240 kg
Weight of three members = 56 kg + 68 kg + 72 kg
= 196 kg
Weight of the fourth member = 240 kg – 196 kg
= 44 kg

Median Calculator is used to compute and display the median of a list of given values or a set of data.

Question 3.
In a class test in mathematics, 10 students scored 75 marks, 12 students scored 60 marks, 8 students scored 40 marks and 3 students scored 30 marks. Find the mean of their score.
Solution:
Total marks of 10 students = 10 × 75 = 750
Total marks of 12 students = 12 × 60 = 720
Total marks of 8 students = 8 × 40 = 320
Total marks of 3 students = 3 × 30 = 90
Total marks of (10 + 12 + 8 + 3) 33 students
= 750 + 720 + 320 + 90
= 1880
Mean of marks = $$\frac{1880}{33}$$
= 56.97 (or) 57 approximately
Aliter:
Total number of students = 10+12 + 8 + 3
= 33
Mean of their marks

= 56.97 (or) 57 approximately

Question 4.
In a research laboratory scientists treated 6 mice with lung cancer using natural medicine. Ten days later, they measured the volume of the tumor in each mouse and given the results in the table.

find the mean.
Solution:

$$\bar { x }$$ = $$\frac{Σfx}{Σf}$$
= $$\frac{2966}{21}$$
= 141.238
= 141.24
The Arithmetic mean = 141.24 mm³

Question 5.
If the mean of the following data is 20.2, then find the value of p.

Solution:

$$\bar { x }$$ = $$\frac{Σfx}{Σf}$$
20.2 = $$\frac{610+20p}{30+p}$$
610 + 20 p = 20.2 (30 + p)
610 + 20 p = 606 + 20.2 p
610 – 606 = 20.2 p – 20 p
4 = 0.2 p
p = $$\frac{4}{0.2}$$
= $$\frac{4×10}{2}$$
= 20
The value of p = 20

Question 6.
In the class, weight of students is measured for the class records. Calculate mean weight of the class students using direct method.

Solution:

Arithmetic mean $$\bar { x }$$ = $$\frac{Σfx}{Σf}$$
= $$\frac{2010}{50}$$
= 40.2
Arithmetic mean = 40.2

Question 7.
Calculate the mean of the following distribution using Assumed Mean Method.

Solution:
Assumed Mean (A) = 25

Arithmetic mean ($$\bar { x }$$) = A+$$\frac{Σfd}{Σf}$$
= 25 + $$\frac{270}{63}$$
= 25 + 4. 29
Assumed Mean = 29.29

Question 8.
Find the Arithmetic Mean of the following data using Step Deviation Method:

Solution:
Assumed Mean (A) = 32

Arithmetic mean = A+$$\frac{Σfd}{Σf}$$ × c
= 32 + ($$\frac{-77.5}{105}$$×4)
= 32 – 2.95
= 29.05
Arithmetic mean = 29.05

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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 3 Algebra Ex 3.15

Multiple Choice Questions.

Question 1.
If x3 + 6x2 + kx + 6 is exactly divisible by x + 2, then k = 2
(a) 6
(b) -7
(c) -8
(d) 11
Solution:
(d) 11
Hint:
p(x) = x3 + 6x2 + kx + 6
Given p(-2) = 0
(-2)3 + 6(-2)2 + k(-2) + 6 = 0
-8 + 24 – 2k + 6 = 0
22 – 2k = 0
k = $$\frac{22}{2}$$
= 11

Question 2.
The root of the polynomial equation 2x + 3 = 0 is…….
(a) $$\frac{1}{3}$$
(b) –$$\frac{1}{3}$$
(c) –$$\frac{3}{2}$$
(d) –$$\frac{2}{3}$$
Solution:
(c) –$$\frac{3}{2}$$
Hint:
2x + 3 = 0
2x = – 3 ⇒ x = –$$\frac{3}{2}$$

Online Polynomial Root Calculator. This online tool calculates the roots of a polynomial. I use this tool to calculate the roots to plot Bode diagrams.

Question 3.
The type of the polynomial 4 – 3x3 is ……..
(a) constant polynomial
(b) linear polynomial
(d) cubic polynomial
Solution:
(d) cubic polynomial

Question 4.
If x51 + 51 is divided by x + 1, then the remainder is …….
(a) 0
(b) 1
(c) 49
(d) 50
Solution:
(d) 50
Hint:
p(x) = x51 + 51
p(-1)= (-1)51 + 51
= -1 + 51
= 50

Question 5.
The zero of the polynomial 2x + 5 is ……..
(a) $$\frac{5}{2}$$
(b) –$$\frac{5}{2}$$
(c) $$\frac{2}{5}$$
(d) –$$\frac{2}{5}$$
Solution:
(b) –$$\frac{5}{2}$$
Hint:
2x + 5 = 0 ⇒ 2x = -5 ⇒ x = –$$\frac{5}{2}$$

Question 6.
The sum of the polynomials p(x) = x3 – x2 – 2, q(x) = x2 – 3x + 1
(a) x3 – 3x – 1
(b) x3 + 2x2 – 1
(c) x3 – 2x2 – 3x
(d) x3 – 2x2 + 3x – 1
Solution:
(a) x3 – 3x – 1
Hint:
p(x) + q(x) = (x3 – x2 – 2) + (x2 – 3x + 1) = x3 – x2 – 2 + x² – 3x + 1
= x³ – 3x – 1

Question 7.
Degree of the polynomial (y³ – 2) (y³ + 1) is
(a) 9
(b) 2
(c) 3
(d) 6
Solution:
(d) 6
(y³ – 2) (y³ + 1) = y6 + y³ – 2y³ – 2
= y6 – y³ – 2

Question 8.
Let the polynomials be
(A) -13q5 + 4q² + 12q
(B) (x² + 4)(x² + 9)
(C) 4q8 – q6 + q²
(D) –$$\frac{5}{7}$$ y12 + y³ + y5.
Then ascending order of their degree is
(a) A, B, D, C
(b) A, B, C, D
(c) B, C, D, A
(d) B, A, C, D
Solution:
(d) B, A, C, D

Question 9.
If p(a) = 0 then (x – a) is a …….. of p(x)
(a) divisor
(b) quotient
(c) remainder
(d) factor
Solution:
(d) factor

Question 10.
Zeros of (2 – 3x) is ……..
(a) 3
(b) 2
(c) $$\frac{2}{3}$$
(d) $$\frac{3}{2}$$
Solution:
(c) $$\frac{2}{3}$$

Question 11.
Which of the following has x -1 as a factor?
(a) 2x – 1
(b) 3x – 3
(c) 4x – 3
(d) 3x – 4
Solution:
(b) 3x – 3

Question 12.
If x – 3 is a factor of p(x), then the remainder is ……..
(a) 3
(b) -3
(c) p(3)
(d) p(-3)
Solution:
(c) p(3)

Question 13.
(x +y)(x² – xy + y²) is equal to ……..
(a) (x + y)³
(b) (x – y)³
(c) x³ + y³
(d) x³ – y³
Solution:
(c) x³ + y³

Question 14.
(a + b – c)² is equal to ……..
(a) (a – b + c)²
(b) (-a – b + c)²
(c) (a + b + c)²
(d) (a – b – c)²
Solution:
(b) (-a – b + c)²
Hint:
(a + b – c)² = a² + b² + c² + 2ab – 2bc – 2ac
(- a – b + c)² = a² + b² + c² + 2ab – 2bc – 2ac
(OR)
(- a – b + c)² = (-1)² (a + b + c)² (taking – 1 as common)
= (a + b – c)²

Question 15.
In an expression ax² + bx + c the sum and product of the factors respectively ……..
(a) a, bc
(b) b, ac
(c) ac, b
(d) bc, a
Solution:
(b) b, ac

Question 16.
If (x + 5) and (x – 3) are the factors of ax² + bx + c, then values of a, b and c are ………
(a) 1, 2, 3
(b) 1, 2, 15
(c) 1, 2, -15
(d) 1, -2, 15
Solution:
(c) 1, 2, -15
Hint:
(x + 5) (x – 3) = x² + (5 – 3) x + (5) (-3)
= x² + 2x – 15
compare with ax² + bx + c
a = 1, b = 2 and c = -15

Question 17.
Cubic polynomial may have maximum of ……… linear factors.
(a) 1
(b) 2
(c) 3
(d) 4
Solution:
(c) 3

Question 18.
Degree of the constant polynomial is ……..
(a) 3
(b) 2
(c) 1
(d) 0
Solution:
(d) 0

Question 19.
Find the value of m from the equation 2x + 3y = m. If its one solution is x = 2 and y = -2.
(a) 2
(b) -2
(c) 10
(d) 0
Solution:
(b) – 2
Hint:
The equation is 2x + 3y = m
Substitute x – 2 and y = -2 we get
2(2) + 3(-2) = m ⇒ 4 – 6 = m ⇒ -2 = m

Question 20.
Which of the following is a linear equation?
(a) x + $$\frac{1}{2}$$ = 2
(b) x (x – 1) = 2
(c) 3x + 5 = $$\frac{2}{3}$$
(d) x³ – x = 5
Solution:
(c) 3x + 5 = $$\frac{2}{3}$$

Question 21.
Which of the following is a solution of the equation 2x – y = 6?
(a) (2, 4)
(b) (4, 2)
(c) (3, -1)
(d) (0, 6)
Solution:
(b) (4, 2)
Hint:
2x – y = 6
Substitute x – 4 and y = 2 we get
2(4) – 2 = 6 ⇒ 8 – 2 = 6 ⇒ 6 = 6
∴ (4, 2) is the solution

Question 22.
If (2, 3) is a solution of linear equation 2x + 3y = k then, the value of k is ……..
(a) 12
(b) 6
(c) 0
(d) 13
Solution:
(d) 13
Hint:
The equation is 2x + 3y = k
Substitute x = 2 and y = 3 we get,
2(2) + 3(3) = k ⇒ 4 + 9 = k ⇒ 13 = k

Question 23.
Which condition does not satisfy the linear equation ax + by + c = 0 ……..
(a) a ≠ 0, b = 0
(b) a = 0, b ≠ 0
(c) a = 0, b = 0, c ≠ 0
(d) a ≠ 0, b ≠ 0
Solution:
(c) a = 0, b = 0, c ≠ 0

Question 24.
Which of the following is not a linear equation in two variable?
(a) ax + by + c = 0
(b) 0x + 0y + c = 0
(c) 0x + by + c = 0
(d) ax + 0y + c = 0
Solution:
(b) 0x + 0y + c = 0
Hint:
0x + 0y + c = 0
0 + 0 + c = 0 ⇒ c = 0
There is no variable.
∴ It is not a linear equation

Question 25.
The value of k for which the pair of linear equations 4x + 6y – 1 = 0 and 2x + ky – 1 = 0 represents parallel lines is ……..
(a) k = 3
(b) k = 2
(c) k = 4
(d) k = -3
Solution:
(a) k = 3
Hint:
Slope of 4x + 6y – 1 = 0 is
6y = -4x + 1 ⇒ y = $$\frac{-4}{6}$$ x + $$\frac{1}{6}$$
Slope = $$\frac{-4}{6}$$ = $$\frac{-2}{3}$$
Slope of 2x + ky – 7 = 0
ky = -2x + 7
y = $$\frac{-2}{k}$$x + $$\frac{7}{k}$$
Slope of a line = $$\frac{-2}{k}$$
Since the lines are parallel
$$\frac{-2}{3}$$ = $$\frac{-2}{k}$$
-2k = – 6
k = $$\frac{6}{2}$$
= 3

Question 26.
A pair of linear equations has no solution then the graphical representation is ……..

Solution:

Hint:
Since there is no solution the two lines are parallel. (l11m)

Question 27.
If $$\frac{a_1}{a_2}$$ ≠ $$\frac{b_1}{b_2}$$ where a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 then the given pair of linear equation has …….. solution(s).
(a) no solution
(b) two solutions
(c) unique
(d) infinite
Solution:
(c) unique
Hint:
Since it has unique solution
$$\frac{a_1}{a_2}$$ ≠ $$\frac{b_1}{b_2}$$

Question 28.
$$\frac{a_1}{a_2}$$ = $$\frac{b_1}{b_2}$$ ≠ $$\frac{c_1}{c_2}$$ where a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 then the given pair of linear equation has …….. solution(s).
(a) no solution
(b) two solutions
(c) infinite
(d) unique
Solution:
(a) no solution
Hint:
$$\frac{a_1}{a_2}$$ = $$\frac{b_1}{b_2}$$ ≠ $$\frac{c_1}{c_2}$$ the linear equation has no solution.

Question 29.
GCD of any two prime numbers is …….
(a) -1
(b) 0
(c) 1
(d) 2
Solution:
(c) 1

Question 30.
The GCD of x4 – y4 and x² – y² is ……..
(a) x4 – y4
(b) x² – y²
(c) (x + y)²
(d) (x + y)4
Solution:
(b) x² – y²
Hint:
x4 – y4 = (x²)² – (y²)²
= (x² + y²)(x² – y²)
x² – y² = (x² – y²)
G.C.D. = x² – y²