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

### Samacheer Kalvi 10th Science Laws of Motion Text Book Back Questions and Answers

Question 1.
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)
(c) mass of the object

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.
(c) change of momentum

Question 3.
Newton’s III law is applicable:
(a) for a body is at rest
(b) for a body in motion
(c) both (a) & (b)
(d) only for bodies with equal masses
(b) for a body in motion

Question 4.
Plotting a graph for momentum on the X-axis and time on Y-axis. Slope of momentum – time graph gives _____
(a) Impulsive force
(b) Acceleration
(c) Force
(d) Rate of force.
(c) Force

Question 5.
In which of the following sport the turning effect of force is used?
(a) swimming
(b) tennis
(c) cycling
(d) hockey
(c) cycling

Question 6.
The unit of ‘g’ is ms-2. It can be also expressed as:
(a) cm s-2
(b) N kg-1
(c) N m2kg-1
(d) cm2s-2
(a) cm s-2

Question 7.
One kilogram force equals to _____ .
(a) 9.8 dyne
(b) 9.8 × 104 N
(c) 98 × 104 dyne
(d) 980 dyne.
(c) 98 × 104 dyne

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) 4 M
(b) 2 M
(c) M/4
(d) M
(c) M/4

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%
(c) decrease by 25%

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.
(d) both a and c.

II. Fill in the blanks

1. To produce a displacement …….. is required.
2. Passengers lean forward when the sudden brake is applied in a moving vehicle. This can be explained by ……….
3. By convention, the clockwise moments are taken as ……… and the anticlockwise moments are taken as ……….
4. …….. is used to change the speed of the car.
5.  A man of mass 100 kg has a weight of …….. at the surface of the Earth.

1. force
2. inertia
3. negative, positive
4. Accelerator
5. Weight = m × g = 100 × 9.8 = 980 N

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

1. The linear momentum of a system of particles is always conserved.
2. Apparent weight of a person is always equal to his actual weight.
3. Weight of a body is greater at the equator and less at the polar region.
4. Turning a nut with a spanner having a short handle is so easy than one with a long handle.
5. There is no gravity in the orbiting space station around the Earth. So the astronauts feel weightlessness.

1. True
2. False – Apparent weight of a person is not always equal to his actual weight.
3. False – Weight of a body is minimum at the equator. It is maximum at the poles.
4. False – Turning a nut with a spanner having a longer handle is so easy than one with a short handle.
5. False – Astronauts are falling freely around the earth due to their huge orbital velocity.

IV. Match the following.

A. (ii)
B. (Hi)
C. (iv)
D. (i)

V. Assertion and 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.
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.
2. Assertion: The value of ‘g’ decreases as height and depth increases from the surface of the Earth.
Reason: ‘g’ depends on the mass of the object and the Earth.
1. (b)
2. (c)

Question 1.
Define inertia. Give its classification.
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’.
Classifications:

1. Inertia of rest
2. Inertia of motion
3. Inertia of direction

Question 2.
Classify the types of force based on their application.
Based on the direction in which the forces act, they can be classified into two types as:

1. Like parallel forces: Two or more forces of equal or unequal magnitude acting along the same direction, parallel to each other are called like parallel forces.
2. Unlike parallel forces: If two or more equal forces or unequal forces act along with opposite directions parallel to each other, then they are called, 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.
F1 = 5 N
F2 = 15 N
∴ Resultant force FR = F1 – F2
= 5 – 15 = -10 N
It acts in the direction of the force of 15 N (F2).

Question 4.
Differentiate mass and weight.
Ratio of masses of planets is
m1 = m2 = 2 : 3
R1 = R2 = 4 : 7
We know

Question 5.
Define the moment of a couple.
When two equal and unlike parallel forces applied simultaneously at two distinct points constitute a couple. A couple results in causes the rotation of the body. This rotating effect of a couple is known as the moment of a couple.

Question 6.
State the principle of moments.
Principle of moments states that if a rigid body is in equilibrium on the action of a number of like (or) unlike parallel forces 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.
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?
When a spanner is having a long handle, the turning effect of the applied force is more when the distance between the fixed edge and the point of application of force is more. Hence a spanner with a long handle is preferred to tighten screws in heavy vehicles.

Question 9.
While catching a cricket ball the fielder lowers his hands backwards. Why?
While catching a cricket ball the fielder lowers his hands backwards, so increase the time during which the velocity of the cricket ball decreases to zero. Therefore the impact of force on the palm of the fielder will be reduced.

Question 10.
How does an astronaut float in a space shuttle?
Astronauts are not floating but falling freely around the earth due to their huge orbital velocity. Since spaceshuttle and astronauts have equal acceleration, they are under free fall condition. (R = 0) Hence, both the astronauts and the space station are in the state of weightlessness.

VII. Solve the given problems.

Question 1.
Two bodies have a mass ratio of 3 : 4 The force applied on the bigger mass produces an acceleration of 12 ms2. What could be the acceleration of the other body, if the same force acts on it.
Ratio of masses m1 : m2 = 3 : 4
Acceleration of m2 is a2 = 12 m/s²
Force acting of m2 is F2 = m2a2
F2 = 4 × 12 = 48N
but F2 = F1
∴ Force acting on m1 is F1 = 48N
∴ Acceleration of m1 = a1 = $$\frac{F_1}{m_1}$$
a1 = $$\frac{48}{3}$$
= 16 m/s²
Acceleration of the other body ax = 16 m/s²

Question 2.
A ball of mass 1 kg moving with a speed of 10 ms-1 rebounds after a perfect elastic collision with the floor. Calculate the change in linear momentum of the ball.
Given mass = 1 kg, speed = 10 ms-1
Initial momentum = mu = 1 × 10 = 10 kg ms-1
Final momentum = -mu = -10 kg ms-1
Change in momentum = final momentum – initial momentum = -mu – mu
Change in momentum = -20 kg ms-1

Question 3.
A mechanic unscrew 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?
Force acting on the screw F1 = 140 N
Length of a spanner d1 = 40 × 10-2 m
Second force applied to the screw F2 = 40 N
Let the length of spanner be d2
According to the Principle of moments,
F1 × d1 = F2 × d2
= 140 × 40 = 40 × d2
∴ d2 = $$\frac{140×40}{40}$$
= 140 × 10-2 m
Length of a spanner = 140 × 10-2 m

Question 4.
The ratio of masses of two planets is 2 : 3 and the ratio of their radii is 4 : 7. Find the ratio of their accelerations due to gravity.
Ratio of masses of two planets is
m1 : m2 = 2 : 3
R1 : R2 = 4 : 7
We know g
Img 2
∴ g1 : g2 = 49 : 24

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

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

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

Question 2.
State Newton’s laws of motion.
(i) Newton’s First Law : States that “every body 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”.

(ii) Newton’s Second Law : States that “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”.

(iii) Newton’s third law : States that “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.
Let, ‘m’ be the mass of a moving body, moving along a straight line with an initial speed V. 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 Pi = mu
Final momentum of the body Pf = mv
Change in momentum Δp = Pi – Pf – mv – mu
By Newton’s second law of motion,
Force, F ∝ rate of change of momentum
F ∝ change in momentum / time
F ∝ $$\frac{mv-mu}{t}$$
F = $$\frac {km(v-u)}{t}$$
Here, k is the proportionality constant.
k = 1 in all systems of units. Hence,
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

Question 4.
State and prove the law of conservation of linear momentum.

Proof:
Let two bodies A and B having masses m1 and m2 move with initial velocity u1 and u2 in a straight line. Let the velocity of the first body be higher than that of the second body, i.e,, u1 > u2. 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,
FB = m2(v2 – u2)/t
Force on body A due to B,
FA = m1(v1 – u1)/t
By Newton’s III law of motion,
Action force = Reaction force
FA = -FB
m1(v1 – u1)/t = -m2 (v2 – u2)/t
m1 v1 + m2 v2 = m1 u1 + m2 u2
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 of linear momentum is proved.

Question 5.
Describe rocket propulsion.

1. Propulsion of rockets is based on the law of conservation of linear momentum as well as Newton’s III law of motion.
2. Rockets are filled with fuel (either liquid or solid) in the propellant tank. When the rocket is fired, this fuel is burnt and hot gas is ejected with high speed from the nozzle of the rocket, producing a huge momentum.
3. To balance this momentum, an equal and opposite reaction force is produced in the combustion chamber, which makes the rocket project forward.
4. While in motion, the mass of the rocket gradually decreases, until the fuel is completely burnt out.
5. Since there is no net external force acting on it, the linear momentum of the system is conserved.
6. The mass of the rocket decreases with altitude, which results in the gradual increase in the velocity of the rocket.
7. 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.
Newton’s universal law of gravitation 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.

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/r²
On combining the above two expressions
F ∝ $$\frac{m_1×m_2}{r^2}$$
F = $$\frac{Gm_1 m_2}{r^2}$$
Where G is the universal gravitational constant. Its value in SI unit is 6.674 × 10-11 N m² kg-2.

Question 7.
Give the applications of gravitation.

1. Dimensions of the heavenly bodies can be measured using the gravitation law. Mass of the Earth, the radius of the Earth, acceleration due to gravity, etc. can be calculated with higher accuracy.
2. Helps in discovering new stars and planets.
3. 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.
4. Helps to explain germination of roots is due to the property of geotropism, which is the property of a root responding to the gravity.
5. 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.
Mass of first block m1 = 8 kg
Mass of second block m2 = 2 kg
Total mass M = 8 + 2 = 10 kg
Force applied F = 15 N
∴ Acceleration a = $$\frac{F}{M}$$
$$\frac{15}{10}$$ = 1.5 m/s²
Force exerted on the 2 kg mass,
F = ma
= 2 × 1.5 = 3 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)
Let the mass of truck be m1
Let the mass of bike be m2
m1 = 4m2
∴ $$\frac{m_1}{m_2}$$ = 4
Kinetic energy K.E1 = K.E2
∴ m2, $${ v }_{ 1 }^{ 2 }$$ = m2$${ v }_{ 1 }^{ 2 }$$

Ratio of momenta be P1 : P2

∴ Ratio of their momenta = 2 : 1

Question 3.
“Wearing helmet and fastening the seat belt is highly recommended for safe journey” Justify your answer using Newton’s laws of motion.
(i) According to Newton’s Second Law, when you fall from a bike on the ground with a force equal to your mass and acceleration of the bike.
According to Newton’s Third Law, an equal and opposite reacting force on the ground is exerted on your body. When you do not wear a helmet, this reacting force can cause fatal head injuries. So it is important to wear helmet for a safe journey.

(ii) Inertia in the reason that people in cars need to wear seat belts. A moving car has inertia, and so do the riders inside it. When the driver applies the brakes, an unbalanced force in applied to the car. Normally the bottom of the seat applies imbalanced force friction which slows the riders down as the car slows. If the driver stops the car suddenly, however, this force is not exerted over enough time to stop the motion of the riders. Instead, the riders continue moving forward with most of their original speed because of their inertia.

### Samacheer Kalvi 10th Science Laws of Motion Additional Important Questions and Answers

Question 1.
When a force is exerted on an object, it can change its:
(a) state
(b) shape
(c) position
(d) all the above
(d) all the above

Question 2.
When the train stops, the passenger moves forward, It is due to ______ .
(a) Inertia of passenger
(b) Inertia of train
(c) gravitational pull by the earth
(d) None of the above.
(a) Inertia of passenger

Question 3.
Force is a …….. quantity.
(a) vector
(b) fundamental
(c) scalar
(d) none
(a) vector

Question 4.
The force of gravitation is ________ .
(a) repulsive
(b) conservative
(c) electrostatic
(d) non – conservative.
(b) conservative

Question 5.
The laws of motion of a body is given by:
(a) Galileo
(b) Archimedis
(c) Einstein
(d) Newton
(d) Newton

Question 6.
A bodyweight 700 N on earth. What will be its weight on a planet having 1 / 7 of earth’s mass and half of the earth’s radius?
(a) 400 N
(b) 300 N
(c) 200 N
(d) 100 N.
(a) 400 N

Question 7.
From the following statements write down that which is not applicable to mass of an object:
(a) It is a fundamental quantity
(b) It is measured using physical balance
(c) It is measured using spring balance
(d) It is the amount of matter.
(c) It is measured using spring balance

Question 8.
Newton’s first law of motion defines:
(a) inertia
(b) force
(c) acceleration
(d) both inertia and force
(d) both inertia and force

Question 9.
Mechanics is divided into ____ types.
(a) one
(b) two
(c) three
(d) four.
(b) two

Question 10.
When an object undergoes acceleration:
(a) its velocity increases
(b) its speed increases
(c) its motion is uniform
(d) a force always acts on it
(d) a force always acts on it

Question 11.
On what factor does inertia of a body depend?
(a) volume
(b) area
(c) mass
(d) density
(c) mass

Question 12.
_____ deals with the motion of bodies without considering the cause of motion.
(a) Inertia
(b) Force
(c) Kinematics
(d) kinetics.
(c) Kinematics

Question 13.
If mass of an object is m, velocity v, acceleration a and applied force is F and momentum P is given by:
(a) P = m × v
(b) P = m × a
(c) P = $$\frac{m}{v}$$
(d) P = $$\frac{v}{m}$$
(a) P = m × v

Question 14.
Which of the following is a vector quantity?
(a) speed
(b) distance
(c) momentum
(d) time
(c) momentum

Question 15.
Unit of momentum in SI system is ______ .
(a) ms-1
(b) Kg ms-2
(c) Kg ms-1
(d) ms-2
(c) Kg ms-1

Question 16.
Force is measured based on:
(a) Newton’s first law
(b) Newton’s second law
(c) Newton’s third law
(d) All the above
(b) Newton’s second law

Question 17.
Force measures rate of change of:
(a) acceleration
(b) velocity
(c) momentum
(d) distances
(c) momentum

Question 18.

The rotating or turning effect of a force about a fixed point or fixed axis is called _____ .
(a) Force
(b) momentum
(c) torque
(d) couples.
(c) torque

Question 19.
The physical quantity which is equal to the rate of change of momentum is:
(a) displacement
(b) acceleration
(c) force
(d) impulse
(c) force

Question 20.
The momentum of a massive object at rest is:
(a) very large
(b) very small
(c) zero
(d) infinity
(c) zero

Question 21.
The velocity which is sufficient to just escape from the gravitational pull of the earth is _____ .
(a) drift velocity
(b) escape velocity
(d) final velocity.
(b) escape velocity

Question 22.
A force applied on an object is equal to:
(a) product of mass and velocity
(b) sum of mass and velocity of an object
(c) product of mass and acceleration
(d) sum of mass and acceleration
(c) product of mass and acceleration

Question 23.
Action and reaction do not balance each other because they:
(a) act on the same body
(b) do not act on the same body
(c) are in opposite direction
(d) are unequal
(b) do not act on the same body

Question 24.
The value of variation of accelaration due to gravity (g) is ______ at the centre of the earth.
(a) one
(b) zero
(c) ∞
(d) $$\frac{1}{\infty}$$.
(b) zero

Question 25.
Action and reaction forces are:
(a) equal in magnitude
(b) equal in direction
(c) opposite in direction
(d) both equal in magnitude and opposite in direction
(d) both equal in magnitude and opposite in direction

Question 26.
If mass of a body is doubled then its acceleration becomes:
(a) halved
(b) doubled
(c) thrice
(d) zero
(a) halved

Question 27.
The principle involved in the working of a jet plane is:
(a) Newton’s first law
(b) Conservation of momentum
(c) Law of inertia
(d) Newton’s second law
(b) Conservation of momentum

Question 28.
_____ of a body is defined as the quantity of matter contained in the object.
(a) weight
(b) mass
(c) force
(d) momentum.
(b) mass

Question 29.
A gun gets kicked back when a bullet is fired. It is a good example of Newton’s:
(a) gravitational law
(b) first law
(c) second law
(d) third law
(d) third law

Question 30.
To change the state or position of an object force is essential.
(a) balanced
(b) unbalanced
(c) electric
(d) elastic
(b) unbalanced

Question 31.
When a bus starts suddenly the passengers in the standing position are pushed backwards, this action is due to:
(a) first law of motion
(b) second law of motion
(c) third law of motion
(d) conservation of momentum
(a) first law of motion

Question 32.
When a body at rest breaks into two pieces of equal masses, then the parts will move:
(a) in same direction
(b) along different directions
(c) in opposite directions with unequal speeds
(d) in opposite directions with equal speeds
(d) in opposite directions with equal speeds

Question 33.
The principle of function of a jet aeroplane is based on:
(a) first law of motion
(b) second law of motion
(c) third law of motion
(d) all the above
(c) third law of motion

Question 34.
Which of the following has the largest inertia?
(a) pin
(b) book
(c) pen
(d) table
(d) table

Question 35.
An athlete runs a long path before taking a long jump to increase:
(a) energy
(b) inertia
(c) momentum
(d) force
(c) momentum

Question 36.
The weight of a person is 50 kg. The weight of that person on the surface
(a) 50 N
(b) 35 N
(c) 380 N
(d) 490 N
(d) 490 N

Question 37.
Which is incorrect statement about the action and reaction referred to Newton’s third law of motion?
(a) They are equal
(b) They are opposite
(c) They act on the same object
(d) They act on two different objects
(c) They act on the same object

Question 38.
The tendency of a force to rotate a body about a given axis is called:
(a) turning effect of a force
(b) moment of force
(c) torque
(d) all the above
(d) all the above

Question 39.
The magnitude of the moment of force is:
(a) product of force and the perpendicular distance
(b) product of force and velocity
(c) ratio of force to the acceleration
(d) ratio of force to the perpendicular distance
(a) product of force and the perpendicular distance

Question 40.
If the force rotates the body in the anticlockwise direction, then the moment is called:
(a) clockwise moment
(b) anticlockwise moment
(c) couple
(d) torque
(b) anticlockwise moment

Question 41.
Anticlockwise moment is:
(a) positive
(b) negative
(c) opposite
(d) zero
(a) positive

Question 42.
Clockwise moment or torque is:
(a) zero
(b) always one
(c) negative
(d) positive
(c) negative

Question 43.
SI unit of moment of force is:
(a) Nm-2
(b) Nm-1
(c) Ns
(d) Nm
(d) Nm

Question 44.
Moment of force produces:
(a) acceleration
(b) linear motion
(c) velocity
(d) angular acceleration
(d) angular acceleration

Question 45.
Two equal and opposite forces whose lines of action do not coincide are said to constitute a:
(a) couple
(b) torque
(c) unlike force
(d) parallel force
(a) couple

Question 46.
Couple produces:
(a) translatory motion
(b) rotatory motion
(c) translatory as well as rotatory motion
(d) neither translatory nor rotatory
(b) rotatory motion

Question 47
……. is an example of couple.
(a) opening or closing a tap
(b) turning of a key in a lock
(c) steering wheel of car
(d) all the above
(d) all the above

Question 48.
Force of attraction between any two objects in the universe is called:
(a) gravitational force
(b) mechanical force
(c) magnetic force
(d) electrostatic force
(a) gravitational force

Question 49.
Universal law of gravitation was given by:
(a) Archimedes
(b) Aryabhatta
(c) Kepler
(d) Newton
(d) Newton

Question 50.
The force of gravitation between two bodies does not depend on:
(a) product of their masses
(b) their separation
(c) sum of their masses
(d) gravitational constant
(c) sum of their masses

Question 51.
Law of gravitation is applicable to:
(a) heavy bodies only
(b) small sized objects
(c) light bodies
(d) objects of any size
(d) objects of any size

Question 52.
The value of gravitational constant (G) is:
(a) different at different places
(b) same at all places in the universe
(c) different at all places of earth
(d) same only at all the places of earth
(b) same at all places in the universe

Question 53.
The unit of gravitational constant is:
(a) Nm² kg
(b) kgms-2
(c) Nm² kg-2
(d) ms-2
(c) Nm² kg-2

Question 54.
The weight of an object is:
(a) the quantity of matter it contains
(b) its inertia
(c) same as its mass
(d) the force with which it is attracted by the earth
(d) the force with which it is attracted by the earth

Question 55.
In vacuum, all freely failing objects have the same:
(a) speed
(b) velocity
(c) force
(d) acceleration
(d) acceleration

Question 56.
The acceleration due to gravity:
(a) has the same value everywhere in space
(b) has the same value everywhere on earth
(c) varies with the latitude on earth
(d) is greater on moon due to its smaller diameter
(c) varies with the latitude on earth

Question 57.
When an object is thrown up, the force of gravity:
(a) is opposite to the direction of motion
(b) is in the same direction as direction of motion
(c) decreases as it rises up
(d) increases as it rises up
(a) is opposite to the direction of motion

Question 58.
The SI unit of acceleration due to gravity ‘g’ is:
(a) ms-1
(b) ms
(c) ms-2
(d) ms²
(c) ms-2

Question 59.
What happens to the value of ‘g’ as we go higher from surface of earth?
(a) decreases
(b) increases
(c) no change
(d) zero
(a) decreases

Question 60.
Mass of a body on moon is:
(a) the same as that on the earth
(b) $$\frac{1}{6}$$th of that at the surface of the earth
(c) 6 times as that on the earth
(d) none of these
(a) the same as that on the earth

Question 61.
At which place is the value of ‘g’ is zero?
(a) at poles
(b) at centre of the earth
(c) at equator
(d) above the earth
(b) at centre of the earth

Question 62.
The weight of the body is maximum:
(a) at the centre of the earth
(b) on the surface of earth
(c) above the surface of earth
(d) none of the above
(b) on the surface of earth

Question 63.
A rock is brought from the surface of the moon to the earth, then its:
(a) weight will change
(b) mass will change
(c) both mass and weight will change.
(d) mass and weight will remain the same
(a) weight will change

Question 64.
Why is the acceleration due to gravity on the surface of the moon is lesser than that on the surface of earth?
(a) because mass of moon is less
(b) radius of moon is less
(c) mass and radius of moon is large
(d) mass and radius of moon is less
(d) mass and radius of moon is less

Question 65.
if the distance between two bodies is doubled, then the gravitational force between them is:
(a) halved
(b) doubled
(c) reduced to one-fourth
(d) increased by one fourth
(c) reduced to one-fourth

Question 66.
The unit newton can also be written as:
(a) kgm
(b) kgms-1
(c) kgms-2
(d) kgm-2s
(c) kgms-2

Question 67.
A bus starts for rest and moves after 4 seconds. Its velocity is 100 ms 1. Its uniform acceleration is:
(a) 10 ms-2
(b) 25 ms-2
(c) 400 ms-2
(d) 2.5 ms-2
(b) 25 ms-2

Question 68.
A body of mass 10 kg increases its velocity from 2 m/s to 8 m/s within 4 second by the application of a constant force. The magnitude of the applied force is:
(a) 1.5 N
(b) 30 N
(c) 15 N
(d) 150 N
(c) 15 N

Question 69.
The moment of force in clockwise direction is the moment in the anticlockwise direction.
(a) equal to
(b) lesser than
(c) greater than
(d) none
(a) equal to

Question 70.
Which one of the following is scalar quantity?
(a) momentum
(b) moment of force
(c) speed
(d) velocity
(c) speed

Question 71.
Which of the following changes the direction of motion of a body?
(a) momentum
(b) force
(c) energy
(d) mass
(b) force

Question 72.
When one makes a sharp turns while driving a car he tends to lean sideways due to:
(a) inertia
(b) inertia of rest
(c) inertia of motion
(d) inertia of direction
(d) inertia of direction

Question 73.
The unit of momentum is:
(a) kg m
(b) m/s²
(c) kg m/s
(d) joule
(c) kg m/s

Question 74.
Moment of a force is given by τ =
(a) $$\frac{F}{d}$$
(b) F × 2d
(c) $$\frac{F}{d}$$
(d) F × d
(d) F × d

Question 75.
Which of the following work on the principle of torque?
(a) Gears
(b) Seasaw
(c) steering wheel
(d) all the above
(d) all the above

Question 76.
The SI unit of gravitational constant
(a) Nm²/g
(b) Nm²kg²
(c) Nm²/g-2
(d) Nmkg
(c) Nm²/g-2

Question 77.
What is the value of gravitational constant?
(a) 6.674 × 10-11 Nm²/g-2
(b) 9.8 × 10-11 Nm²/g-2
(c) 6.647 × 10-11 Nm²/g-2
(d) 13.28 × 10-11 Nm²/g-2
(a) 6.674 × 10-11 Nm²/g-2

Question 78.
The value of mass of the Earth is:
(a) 6.972 × 1024 kg
(b) 6.792 × 1024 kg
(c) 5.972 × 1024 kg
(d) 2.936 × 1024 kg
(c) 5.972 × 1024 kg

Question 79.
At poles of the Earth, weight of the body is:
(a) minimum
(b) maximum
(c) zero
(d) infinity
(b) maximum

Question 80.
Where will the value of acceleration due to gravity be minimum?
(a) poles of the earth
(b) centre of the earth
(c) equator of the earth
(d) space
(d) space

Question 81.
When an elevator is at rest:
(a) Apparent weight is greater than the actual weight
(b) Apparent weight is less than the actual weight
(c) Apparent weight is equal to the actual weight
(d) None of the above
(c) Apparent weight is equal to the actual weight

Question 82.
In a lift, apparent weight of a body is equal to zero when the lift is;
(a) at rest
(b) moving upwards
(c) moving downwards
(d) falling down freely
(d) falling down freely

Question 83.
When the lift is moving upward with an acceleration ‘o’ the apparent weight of the body is:
(a) lesser than actual weight
(b) greater than actual weight
(c) equal to actual weight
(d) zero
(b) greater than actual weight

Question 84.
When an elevator is moving downward, the apparent weight of a person who is in that elevator is:
(a) maximum
(b) zero
(c) minimum
(d) infinity
(c) minimum

Question 85.
Which law helps to predict the path of the astronomical bodies?
(a) Newton’s law of motion
(b) Newton’s law of gravitation
(c) Newton’s law of cooling
(d) Pascal’s law
(b) Newton’s law of gravitation

II. Fill in the blanks.

1. If force – mass × acceleration, then momentum = ………
2. If liquid hydrogen is for rocket, then …….. is for MRI.
3. Inertia: (f) Mass then momentum: ……… Recoil of the gun: (ii) Newton’s third law: then flight of Jet Planes and Rockets: ………
4. Newton’s first law of motion: definition of force and inertia then Newton’s third law of motion: ….(i)….. while Newton’s second law of motion: ……(ii)…….
5. Newton’s first law: qualitative definition of force Newton’s second law: …..(i)…… The value of g: 9.8 ms-2 then Gravitational constant: …..(ii)……
6. Force: vector then momentum: …….(i)……. Balanced force: resultant of the two forces is zero then……(ii)…….. : resultant forces are responsible for change in position or state.
7. Momentum is the product of …….. and …….
8. To produce an acceleration of 1 m/s² in an object of mass 1 kg. The force required is ……… and for 3 kg of mass to produce same acceleration, the force required is ……….
9. Two or more forces are acting in an object and does not change its position, the forces are ………. and it is essential to act some ………. force, to change the state or position of an object.
10. ……… deals with bodies that are at rest under the action of force.
11. A branch of mechanics that deals with the motion of the bodies considering the cause of motion is called ………
12. If m is the mass of a body moving with velocity v then its momentum is given by P = ……..
13. A system of forces can be brought to equilibrium by applying ………. in opposite direction.
14. Torque is a ……… quantity.
15. Steering wheel transfers a torque to the wheels with ………..
16. The mathematical form of the principle of moments is ………..
17. Change in momentum takes place in the ………. of ………
18. 1 Newton = ……..
19. If a force F acts on a body for a time t’s then the impulse is ………
20. 1 kg f = ………
21. The force of attraction between two objects is directly proportional to the product of their ……. and inversely proportional to the square of the ………. between them.
22. The value of g varies with ……… and ………
23. The value of gravitational constant is ……… at all places but the value of acceleration due to gravity ………..
24. The relation between g and G is ………
1. mass × velocity
2. liquid helium
3. (i) Mass and velocity, (ii) Law of conservation of momentum
4. (i) Law of conservation of momentum, (ii) Measure of force
5. (i) Quantitative definition of force, (ii) 6.673 × 10-11 Nm²kg-2
6. (i) vector, (ii) imbalanced force
7. mass, velocity
8. 1 N, 3 N
9. balanced, unbalanced
10. Statics
11. kinetics
12. mv
13. equilibriant
14. vector
15. less effort
16. F1 × d1 = F2 × d2
17. direction, force
18. 105 dyne
19. I = F × t
20. 9.8 N
21. masses, distance
22. altitude, depth
23. same, differs
24. g = $$\frac{GM}{R^2}$$

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

1. Newton’s first law explains inertia:
2. If a motion depends on force then it is called as natural motion.
3. The resistance of a body to change its state of motion is known as inertia of motion.
4. Linear momentum = mass × acceleration.
5. Two equal force acting in opposite directions are called unlike parallel forces.
6. If the resultant force of three force acting on body is zero then the forces are called balanced forces.
7. Torque is a scalar quantity.
8. Moment of couple = Force × ⊥r distance between line of action of forces
9. Principle of moments states that moment in clockwise direction = Moment in anti clockwise direction.
10. 1 Newton = 1 g cm s-2
11. Impulse = Force
12. Propulsion of rockets is based Newton’s third law of motion and conservation of linear momentum.
13. The value of universal gravitational constant is 6.674 × 10-11 Nm² kg-2
14. The relation between g and G is g = $$\frac{Gm}{R^2}$$
15. The value of acceleration due to gravity decreases as the altitude of the body increases.
16. In a ‘free fall’ motion acceleration of the body is equal to the acceleration due to gravity.
1. True
2. False – If a motion does not depend on force then it is called as natural motion.
3. True
4. False – Linear momentum = mass × velocity
5. True
6. True
7. False – Torque is a vector quantity
8. True
9. True
10. False – 1 Newton = 1 kg ms-2
11. False – Impulse = Change in momentum
12. True
13. True
14. False – The relation between g and G is g = $$\frac{GM}{R^2}$$
15. True
16. True

IV. Match the following.

Question 1.
Match the column A with column B.

A. (iv)
B. (i)
C. (iii)
D. (v)
E. (ii)

Question 2.
Match the column A with column B.

A. (iv)
B. (v)
C. (ii)
D. (i)
E. (iii)

Question 3.
Match the column A with column B.

A. (ii)
B. (iv)
C. (v)
D. (i)
E. (iii)

Question 4.
Match the column A with column B.

A. (iv)
B. (v)
C. (i)
D. (ii)

V. Assertion and Reasoning.

Question 1.
Assertion: While travelling in a motor car we tend to remain at rest with respect to the seat.
Reason: While travelling in a motor car we tend to move along the car with respect to the ground.
(a) Both Assertion and Reason are false.
(b) Assertion is true but Reason is false.
(c) Assertion is false but Reason is true.
(d) Both Assertion and Reason are true.
(d) Both Assertion and Reason are true.

Question 2.
Assertion: When we kick a football it will roll over; when we kick a stone of the size of the football, it remains unmoved.
Reason: Inertia of a body depends mainly on its mass.
(a) Both Assertion and Reason are true and Reason explains Assertion.
(b) Both Assertion and Reason are true but Reason doesn’t explain Assertion.
(c) Both Assertion and Reason are false.
(d) Assertion is true but Reason is false.
(a) Both Assertion and Reason are true and Reason explains Assertion.

Question 3.
Assertion: In a gun-bullet experiment, the acceleration of the gun is much lesser than the acceleration of the bullet.
Reason: The gun has much smaller mass than the bullet.
(a) Both Assertion and Reason are false.
(b) Assertion is true but Reason is false.
(c) Assertion is false but Reason is true.
(d) Both Assertion and Reason are true.
(b) Assertion is true but Reason is false.

Question 4.
Assertion: When a bullet is fired from a gun, the bullet moves forward, the gun moves backward.
Reason: Total momentum before collision is equal to the total momentum .after collision.
(a) Both Assertion and Reason are true and Reason explains Assertion.
(b) Both Assertion and Reason are true but Reason doesn’t explain Assertion.
(c) Assertion is true but Reason is false.
(d) Assertion is false but Reason is true.
(b) Both Assertion and Reason are true but Reason doesn’t explain Assertion.

Question 5.
Assertion: A person whose mass on earth is 125 kg will have his mass on moon as 250 kg.
Reason: Mass varies from place to place.
(a) Both Assertion and Reason are true and Reason explains Assertion.
(b) Both Assertion and Reason are true but Reason doesn’t explain Assertion.
(c) Both Assertion and Reason are false.
(d) Assertion is true but Reason is false.
(c) Both Assertion and Reason are false.

Question 6.
Assertion: During turning a cyclist negotiates of the curve, while a man sitting in the car leans outwards of the curve.
Reason: An acceleration is acting towards the centre of the curve.
(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 assertion.
(c) Assertion is true, but the reason is false.
(d) Assertion is false, but the reason is true.
(c) Assertion is true, but the reason is false.

Question 7.
Assertion: On a rainy day, it is difficult to drive a car at high speed.
Reason: The valve of coefficient of friction is lowered due to polishing of the surface.
(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 assertion.
(c) Assertion is true, but the reason is false.
(d) Assertion is false, but the reason is true.
(a) If both the assertion and the reason are true and the reason is the correct explanation of assertion.

Question 8.
Assertion: A rocket moves forward by pushing the air backwards.
Reason: It derives the necessary thrust to move forwarded according to Newton’s third law of motion.
(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 assertion.
(c) Assertion is true, but the reason is false.
(d) Assertion is false, but the reason is true.
(a) If both the assertion and the reason are true and the reason is the correct explanation of assertion.

Question 9.
Assertion: A mass in the elevator which is falling freely, does not experience gravity.
Reason: Inertial and gravitational masses have equivalence.
(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 assertion.
(c) Assertion is true, but the reason is false.
(d) Assertion is false, but the reason is true.
(c) Assertion is true, but the reason is false.

Question 10.
Assertion: The intensity of gravitational field varies with respect to height and depth of a body on the Earth.
Reason: The value of gravitational field intensity depends on height and depth of a body.
(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 assertion.
(c) Assertion is true, but the reason is false.
(d) Assertion is false, but the reason is true.
(d) Assertion is false, but the reason is true.

Question 1.
What is meant by mechanics? How can it be classified?
Mechanics is the branch of physics that deals with the effect of force on bodies. It is divided into two branches namely statics and dynamics.

Question 2.
What is statics?
Statics deals with the bodies, which are at rest under the action of forces.

Question 3.
What is dynamics?
Dynamics is the study of moving bodies under the action of forces.

Question 4.
What is Kinematics?
Kinematics deals with the motion of bodies without considering the cause of motion.

Question 5.
What is Kinetics?
Kinetics deals with the motion of bodies considering the cause of motion.

Question 6.
Define momentum. State its unit.
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.
Its S.I unit is kg ms-1.

Question 7.
What is meant by a force?
Force is one that changes or tends to change the state of rest or of uniform motion of a body.

Question 8.
State the effects of force.

1. Produces or tries to produce the motion of a static body.
2. Stops or tries to stop a moving body.
3. Changes or tries to change the direction of motion of a moving body.

Question 9.
What is resultant force?
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 10.
What are balanced forces?
If the resultant force of all the forces acting on a body is equal to zero, then the body will be in equilibrium. Such forces are called balanced forces.

Question 11.
What are unbalanced forces?
Forces acting on an object which tend to change the state of rest or of uniform motion of it are called unbalanced forces.

Question 12.
What is meant by equilibriant?
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 ‘Equilibriant’.

Question 13.
What is meant by couple? State few examples.
Two equal and unlike parallel forces applied simultaneously at two distinct points constitute a couple. The line of action of the two forces does not coincide.
Eg: Turning a tap, winding or unwinding a screw, spinning of a top, etc.

Question 14.
A sudden application of brakes may cause injury to passengers in a car by collision with panels in front?
With the application of brakes, the car slows down but our body tends to continue in the same state of motion because of inertia.

Question 15.
When we are standing in a bus which begins to move suddenly, we tend to fall backwards. Why?
This is because a sudden start of the bus brings motion to the bus as well as to our feet in contact with the floor of the bus. But the rest of our body opposes this motion because of its inertia.

Question 16.
While travelling through a curved path, passengers in a bus tend to get thrown to one side. Justify.
When an unbalanced force is applied by the engine to change the direction of motion of the bus, passengers move to one side of the seat due to inertia of their body.

Question 17.
Define momentum of an object.
The momentum of an object is defined as the product of its mass and velocity.

Question 18.
Define One newton.
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.

Question 19.
Define one dyne.
The amount of force required for a body of mass 1 gram produces an acceleration of 1 cm s-2, 1 dyne = 1 g cm s-2; also
1 N = 105 dyne.

Question 20.
What is unit force?
The amount of force required to produce an acceleration of 1 ms-2 in a body of mass 1 kg is called ‘unit force’.

Question 21.
What are the values of 1 kg f and 1 g f.
1 kg f= 1 kg × 9.8 m s-2 = 9.8 N;
1 g f = 1 g × 980 cm s-2 = 980 dyne

Question 22.
What is meant by impulsive force?
A large force acting for a very short interval of time is called as ‘Impulsive force’.

Question 23.
What is meant by impulse?
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

Question 24.
Prove that impulse is equal to the magnitude of change in momentum.
By Newton’s second law,
F = ΔP/t (Δ refers to change)
ΔP = F × t
J = ΔP
F × t = ΔP
Impulse is also equal to the magnitude of change in momentum. Its unit is kg ms-1 or N s.

Question 25.
How can the change in momentum be achieved?
Change in momentum can be achieved in two ways. They are:

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

Question 26.
State an example for change in momentum.
Automobiles are fitted with springs and shock absorbers to reduce jerks while moving on uneven roads.

Question 27.
A spring balance is fastened to a wall and another spring balance is attached to its hole and is pulled steadily. Do both the spring balances show different readings on their scales. Give reason.
No, both the spring balances show same reading. Because both action and reaction are equal and opposite.

Question 28.
When a gun is fired it recoils, Give reason.
When a gun is fired it exerts forward force on the bullet. The bullet exerts an equal and opposite reaction force on the gun. This results in the recoil of the gun.

Question 29.
Action and reaction are equal and opposite. But they do not cancel each other. Give reason.
They do not cancel each other because they never act on the same body. Since they act on different bodies, they do not cancel each other.

Question 30.
Why does a cricket player, pulls his arms back with the ball while catching a ball?
(i) The cricket player stops the speeding ball suddenly in a very short time. The high value of velocity of the ball will be decreased to zero, in a very short time and it will result in a high retardation.
(ii) When the player pulls his arms with the ball, he increases the value of time and so retardation is also decreased and retardation force is lesser than before and the palm of player is not hurt.

Question 31.
When a sailor jumps forward, the boat moves backward. State the action and reaction in the above case.
Action – a sailor jumps forward.
Reaction – movement of the boat.

Question 32.
It is easier to stop a tennis ball than a cricket ball moving with the same velocity.
This is because the mass of tennis ball is less than the cricket ball. So it has lesser momentum and hence smaller force is required to stop the tennis ball.

Question 33.
Define moment of force.
The magnitude of the moment of force about a point is defined as the product of the magnitude of force and perpendicular distance of the point from the line of action of the force.

Question 34.
Draw the diagram of a couple.

Question 35.
What do you know about moment of a couple?
Moment of a couple is the product of force and perpendicular distance between the line of action of forces.
M = F × S

Question 36.
It is easier to open a door by applying the force at the free end. Justify.
(i) If the force is applied at the handle of the door to open it, only small force is required. That means larger the perpendicular distance, lesser is the force needed to turn the body.

(ii) From this it is easy to conclude that the turning effect of a body about an axis depends not only on the magnitude of the force but also on the perpendicular distance of the line of action of the applied force from the axis of rotation.

Question 37.
A force can rotate a nut when applied by a wrench.
(a) What is meant by moment of force?
The turning effect of force acting on a body about an axis is called the moment of force.

(b) Name the factors on which the turning effect of a force depend on.
Turning effect of force depends on-

1. The magnitude of the force applied and
2. The distance of line of action of the force from the axis of rotation.

Question 38.
What is meant by weightlessness?
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 39.
What is meant by moment of a force?
The turning effect of force acting on a body about an axis is called moment of force.

Question 40.
What is meant by gravitational force?
The gravitational force is the force of attraction between objects in the universe.

Question 41.
In which direction does gravitational force act?
The gravitational force acts along the line joining the centres of two objects.

Question 42.
(a) When a horse suddenly starts running, the rider falls backward. Give reason.
This is because the lower part of the rider which is in contact with the horse, comes into motion. While his upper part tends to remain at rest due to inertia.

(b) Coin falls into the tumbler when the card is given a sudden jerk. State the fact that is utilized in this illustration.
inertia.

Question 43.
(a) Why it is difficult to walk on a slippery floor or sand?
Because we are unable to push (action) such a ground sufficiently hard. As a result, the force of reaction is not sufficient to help us to move forward.

(b) State the law related to this.
Newton’s third law of motion.

Question 44.
State the numerical value and unit of gravitational constant.
The numerical value of gravitational constant is 6.673 × 10-11 Nm² kg-2.
Its unit is Nm² kg-2.

Question 45.
What is meant by acceleration due gravity?
The acceleration produced in a body on account of the force of gravity is called acceleration due to gravity.

Question 46.
Write the expression of acceleration due to gravity.
Acceleration due to gravity g = $$\frac{GM}{R^2}$$
where G is gravitational constant.
M is the mass of the earth.
R is radius of the earth.

Question 47.
Deduce the value of mass of earth.
Mass of earth M = $$\frac{gR^2}{G}$$
g = 9.8 m/s²
R = 6.38 × 106 m
G = 6.673 × 10-11 Nm² kg-2

= 5.98 × 1024 kg

Question 48.
What happens to the gravitational force between two objects if the masses of both objects are doubled?
If the masses of both objects are doubled, then gravitational force between them will be increased to four times.

Question 49.
The mass of a body is 60 kg. What will be its mass when it is placed on the moon?
The mass of a body on the moon is 60 kg. There will be no change in mass because it is still made up of same amount of matter.

Question 50.
When an object is taken to the moon, is there any change in weight?
Yes. The weight of a object will be decreased because the gravitational force is weak i.e., the value of acceleration due to gravity becomes less on the moon.

Question 51.
Gravitational force acts on all objects is proportional to their masses. But a heavy object falls slower than a light object. Give reason.
It is true that gravitational force between all objects are in proportion to their masses. But in free fall of objects, acceleration produced in a body is due to gravitational force is independent of mass of object that’s why a heavy object does not fall faster.

Question 52.
A falling apple is attracted towards the earth.
(a) Does the apple attract the earth?
Yes. According to Newton’s third Law. The apple attracts the earth.

(b) Why doesn’t earth move towards an apple?
According to Newton’s second Law, for a given force, acceleration a ∝ $$\frac{1}{m}$$. Here mass of an apple is negligibly small compared to earth. So we cannot see the earth moving towards an apple.

Question 53.
Observe the figure and write the answer:

(a) The force which balance A exerts on balance B is called …….
The force which balance A exerts on balance B is called action.

(b) The force of balance B on balance A is called ……..
The force of balance B on balance A is called opposite reaction.

Question 54.
What is meant by apparent weight?
Apparent weight is the weight of the body acquired due to the action of gravity and other external forces acting on the body.

Question 55.
What is meant by free fall?
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’. Here, the apparent weight (R = m (g – g) = 0) of the person is zero.

VII. Solve the given problems.

Question 1.
The ratio of masses of two bodies is 1 : 3 and the ratio of applied forces on them is 4 : 9. Calculate the ratio of their accelerations.
Ratio of masses m1 : m2 = 1 : 3
Ratio of applied forces F1 : F2 = 4 : 9
Accelerations a = $$\frac{F}{m}$$
Acceleration of first body,
a1 = $$\frac{F_1}{m_1}$$
= $$\frac{4}{1}$$ = 4
Acceleration of second body,
a2 = $$\frac{F_2}{m_2}$$
Ratio of their accelerations is 4 : 3

Question 2.
What is acceleration produced by a force of 12 N exerted on an object of mass 3 kg?
F = 12 N; m = 3 kg ; a = ?
F = ma; a = F/m = $$\frac{4}{1}$$ = 4 m/s²
The acceleration produced a = 4 m/s².

Question 3.
A certain force exerted for 1.2 s raises the speed of an object from 1.8 m/s to 4.2 m/s. Later, the same force is applied for 2 s. How much does the speed change in 2 s.
t = 1.2 s; u = 1.8 m/s; v = 4.2 m/s
acceleration a = $$\frac{v-u}{t}$$
= $$\frac{4.2-1.8}{1.2}$$ = $$\frac{2.4}{1.2}$$
= 2 m/s²
Now, the force applied is the same, it will produce the same acceleration.
Change in speed = acceleration × time for which force is applied.
= 2 × 2 = 4 m/s
Change in speed = 4 m/s.

Question 4.
A constant force acts on an object of mass 10 kg for a duration of 4 s. It increases the objects velocity from 2 ms-1 to 8 ms-1. Find the magnitude of the applied force.
Mass of an object m = 10 kg
Initial velocity u = 2 ms-1
Final velocity v = 8 ms-1
We know, force F = $$\frac{m(v-u)}{t}$$
F = $$\frac{10(8-2)}{4}$$
= $$\frac{10×6}{4}$$
= 15 N

Question 5.
Which would require a greater force for accelerating a 2 kg of mass at 4 ms-2 or a 3 kg mass at 2 ms-2?
We know, force F = ma
Given m1 = 2 kg a1 = 4 ms-2
m2 = 3 kg a2 = 2 ms-2
F1 = m1 a1 = 2 × 4 = 8 N
F2 = m2 a2 = 3 × 2 = 6 N
∴ F1 > F2.
Thus, accelerating 2 kg mass at 4 ms-2 would require a greater force.

Question 6.
A bullet of mass 15 g is horizontally fired with a velocity 100 ms-1 from a pistol of mass 2 kg. What is the recoil velocity of the pistol?
The mass of the bullet, m1 = 15 g = 0.015 kg
Mass of the pistol, m2 = 2 kg
Initial velocity of the bullet, u1 = 0
Initial velocity of the pistol, u2 = 0
Final velocity of the bullet, v1 = + 100 ms-1
(The direction of the bullet is taken from left to right-positive, by convention) Recoil velocity of the pistol = v2
Total momentum of the pistol and bullet before firing.
= m1 u1 + m2 u1
= (0.015 × 0) + (2 × 0)
= 0
Total momentum of the pistol and bullet after firing.
= m1 v1 + m2 v2
= (0.015 × 100) + (2 × v2)
= 1.5 + 2v2
According to the law of conservation of momentum,
Total momentum after firing = Total momentum before firing.
1.5 + 2v2 = 0
2v2 = -1.5
v2 = – 0.75 ms-1
Negative sign indicates that the direction in which the pistol would recoil is opposite to that of the bullet, that is, right to left.

Question 7.
A 10 g bullet is shot from a 5 kg gun with a velocity of 400 m/s. what is the speed of recoil of the gun?
Mass of bullet, m1 = 10 g
= 10 × 10-3 kg = 10-2 kg
Mass of gun, m2 = 5 kg
Velocity of bullet, v1 = 400 m/s
speed of recoil of gun v2 = ?
Total momentum of bullet and gun after firing = total momentum before firing.
m1 v1 + m2 v2 = 0
v2 = –$$\frac{m_1 v_1}{m_2}$$
= $$\frac{-10_{-2}×400}{5}$$ = -0.8 m/’s.
The speed of recoil of the gun v2 = -0.8 m/’s.
Negative sign shows that the gun moves in a direction opposite to that of the bullet.

Question 8.
The figure represents two bodies of masses 10 kg and 20 kg, moving with an initial velocity of 10 ms-1 and 5 ms-1 respectively. They collide with each other. After collision, they move with velocities 12 ms-1 and 4 ms-1 respectively. The time of collision is 2 s. Now calculate F2 and F2.

m1 = 10 kg
m2 = 20 kg
u1 = 10 ms-1
u2 = 5 ms-1
v1 = 12 ms-1
v2 = 4 ms-1
Time of collision, t = 2 s
∴ Force acting on 20 kg object
F1 = m2 ($$\frac{v_2-u_2}{t}$$)
= 20($$\frac{4-5}{2}$$)
F1 = -10 N
Force acting on 10 kg object
F2 = m1 ($$\frac{v_1-u_1}{t}$$)
= 10($$\frac{12-10}{2}$$)
F2 = 10 N

Question 9.
The mass of an object is 5 kg. What is its weight on the earth?
Mass, m = 5 kg
Acceleration due to gravity,
g = 9.8 ms-2
Weight, W = m × g
W = 5 × 9.8 = 49 N
Therefore, the weight of the object is 49 N.

Question 10.
Calculate the force of gravitation between two objects of masses 80 kg and 120 kg kept at a distance of 10 m from each other. Given, G = 6.67 × 10-11 Nm² / kg².
m1 = 80 kg, m2 = 120 kg, r = 10 m,
G = 6.67 × 10-11 Nm² / kg², F = ?

= 64.032 × 10-10 N
The force of gravitation between two objects = 64.032 × 10-10 N.

Question 11.
Calculate the value of acceleration due to gravity on moon. Given mass of moon = 7.4 × 1022 kg. radius of moon = 1740 km.

= 1.63 ms2
The acceleration due to gravity = 1.63 ms-2.

Question 12.
State Newton’s law of gravitation. Write an expression for acceleration due to gravity on the surface of the earth. If the ratio of acceleration due to gravity of two heavenly bodies is 1 : 4 and the ratio of their radii is 1 : 3, what will be the ratio of their masses?
Newton’s law of gravitation states that every object in the universe attracts every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
F = $$\frac{Gm_{1}m_{2}}{d^{2}}$$
Acceleration due to gravity g = $$\frac{GM}{R^{2}}$$
Where G is gravitational constant
M is the mass of the earth
R is radius of the earth
Ratio of acceleration due to gravity = 1 : 4
Ratio of radii of two bodies = 1 : 3
Acceleration due to gravity is g

Dividing Equation (1) by equation (2) we get

∴ M1 : M2 = 1 : 36
∴ Ratio of their masses = 1 : 36

Question 13.
A bomb of mass 3 kg, initially at rest, explodes into two parts of 2 kg and 1 kg. The 2 kg mass travels with a velocity of 3 m/s. At what velocity will the 1 kg mass travel?
Mass of a bomb m = 3 kg
Initial velocity of the bomb v = 0
Mass of the first part m1 = 2 kg
Velocity of the first part v1= 3 m/s
Mass of the second part m2 = 1 kg
Let the velocity of the second part be v2.
By the law of conservation of momentum
mv = m1 v1 + m2 v2
3 × 0 = 2 × 3 + 1 × v2
0 = 6 + v2
∴ v2 = -6 m/s
Velocity of the 1 kg mass = -6 m/s

Question 14.
Two ice skaters of weight 60 kg and 50 kg are holding the two ends of a rope. The rope is taut. The 60 kg man pulls the rope with 20 N force. What will be the force exerted by the rope on the other person? What will be their respective acceleration?
Mass of first ice skater = 50 kg
Mass of second ice skater = 60 kg
Force applied by second ice skater = 20 N
When the rope is taut, the force exerted by the rope on the other person is 20 N.

= 0.33 m/s²

Question 1.
Explain the types of forces.
Based on the direction in which the forces act, they can be classified into two types as:
1. Like parallel forces : Two or more forces of equal or unequal magnitude acting along the same direction, parallel to each other are called like parallel forces.
2. Unlike parallel forces : If two or more equal forces or unequal forces act along opposite directions parallel to each other, then they are called unlike parallel forces.

Question 2.
Tabulate the action of forces with their resultant and diagram.

Question 3.
Explain the applications of torque.
1. 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.

2. Seasaw : Most of you have played on the seasaw. 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.

3. Steering Wheel : A small steering wheel enables you to manoeuore a car easily by transferring a torque to the wheels with less effort.

Question 4.
State and explain principle of moments.
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. In other words, at equilibrium, the algebraic sum of the moments of all the individual forces about any point is equal to zero.

In the illustration given in figure, the force F1 produces an anticlockwise rotation at a distance d1 from the point of pivot P (called fulcrum) and the force F2 produces a clockwise rotation at a distance d2 from the point of pivot P. The principle of moments can be written as follows:
Moment of clockwise direction = Moment of anticlockwise direction
F1 × d1 = F2 × d2

Question 5.
Explain the illustrations for Newton’s third law of motion briefly.
Newton’s third law states that ‘for every action, there is an equal and opposite reaction.They always act on two different bodies.
If a body A applies a force FA on a body B, then the body B reacts with force FB on the body A, which is equal to FA in magnitude, but opposite in direction. FB = -FA
Eg:
(i) When birds fly they push the air downwards with their wings (Action) and the air pushes the bird upwards(Reaction).
(ii) When a person swims he pushes the water using the hands backwards (Action), and the water pushes the swimmer in the forward direction (Reaction).
(iii) When you fire a bullet, the gun recoils backward and the bullet is moving forward (Action) and the gun equalises this forward action by moving backward (Reaction).

Question 6.
Derive the relation between acceleration due to gravity (g) and Gravitational constant G.

When a body is at rests on the surface of the Earth, it is acted upon by the gravitational force of the Earth. 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. The entire mass of the Earth is assumed to be concentrated at its centre. 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
F = $$\frac{GMm}{R^2}$$
Here, 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.
According to this law, the force acting on the body is given by the product of its mass and acceleration (called as weight). Here, acceleration of the body is under the action of gravity hence a = g
F = ma = mg …….. (1)
F = weight = mg ……… (2)
Comparing equations (1) and (2), we get
mg = $$\frac{GMm}{R^2}$$
Acceleration due to gravity g = $$\frac{GM}{R^2}$$

Question 7.
Tabulate the apparent weight of person moving in a lift when lift is
(i) moving upwards
(ii) moving downwards
(iii) at rest
(iv) falling down freely.

IX. HOT Questions

Question 1.
What gives the measure of inertia?
Mass of a body gives the measure of inertia.

Question 2.
Is any external force required to keep a body in uniform motion?
No, external force is not required to keep a body in uniform motion.

Question 3.
Which law of motion gives the measure of force?
Newton’s second law of motion.

Question 4.
Write the second law of motion in vector form.
$$\vec { F } =m\vec { a }$$
Where, $$\vec { F }$$ – force, m – mass, $$\vec { a }$$ – acceleration.

Question 5.
What is the net force acting on a cork that floats on water? Why?
The net force is zero, because the weight of the cork is balanced by the upthrust of water on it.

Question 6.
What is the relation between newton and dyne?
1 newton = 105 dyne

Question 7.
A person is standing on a weighing machine placed nearly a door. What will be the effect of the reading of the machine if a person presses the edge of the door upward?
The reading of the machine will increase.

Question 8.
A bomb explode in mid-air into two equal fragments. What is the relation between the direction of motion of the two fragments?
The two fragments will fly off in exactly opposite directions.

Question 9.
Which law explains the following situation, Athlete runs a certain distance before long jump.
Law of inertia which is Newton’s first law of motion.

Question 10.
Is impulse a scalar?
No, impulse is a vector quantity.

Question 11.
When a lift moves with uniform velocity, what is its
(i) acceleration and
(ii) the apparent weight of the person standing inside the lift.