# SELINA Solutions for Class 9 Physics Chapter 3 - Laws of Motion

## Chapter 3 - Laws of Motion Exercise Ex 3(C)

Name the two* *factors on which the force needed to stop a moving body in a given time depends.

Force needed to stop a moving body in a given time depends on its mass and velocity.

The linear momentum of a body of mass m moving with velocity v is given by the following relation:

(a) v/m (b) m/v

(c) mv (d) 1/mv

Mv

A body of mass 5 kg is moving with velocity 2 m s^{-1}. Calculate its linear momentum.

Mass of the body, m = 5kg

Velocity, v = 2 m/s

Linear momentum = mv = (5)(2) kg m/s

= 10 kg m/s^{-1}

Define linear momentum and state its S.I. unit.

Linear momentum of a body is the product of its mass and velocity.

Its SI unit is kgms^{-1}.

The unit of linear momentum is :

(a) N s (b) kg m s^{-2}

(c) N s^{-1} (d) kg^{2} m s^{-1}

N s

The linear momentum of a ball of mass 50 g is 0.5 kg m s^{-1}. Find its velocity.

Linear momentum = 0.5 kg m/s

Mass, m = 50 g = 0.05 kg

Velocity = Linear momentum/mass

= 0.5/0.05 m/s

= 10 m/s ^{-1}

A body of mass *m *moving with a velocity *v *is acted upon by a force. Write an expression for change in momentum in each of the following cases: (i) When *v * c, (ii) When *v *c and (iii) When *v * c but *m *does not remain constant. Here, c is the speed of light.

(i) When vc,

p = (mv) = mv

(ii) When v c,

p = (mv)

(iii) When vc but m does not remain constant.

p = (mv)

The correct form of Newton's second law is given by the following equation:

(a) (b)

(c) (d)

A force of 15 N acts on a body of mass 2 kg. Calculate the acceleration produced.

Force, F = 15 N

Mass, m = 2kg

Acceleration, a = F/m [ From Newton's second law]

Or, a = (15/2) ms^{-2}

Or, a = 7.5 ms^{-2}

Show that the rate of change of momentum = mass × acceleration. Under what condition does this relation hold?

Let a force 'F' be applied on a body of mass m for a time 't' due to which its velocity changes from u to v. Then,

Initial momentum of body = mu

Final momentum of body = mv

Change in momentum of the body in 't' seconds = mv mu = m (vu)

Rate of change of momentum = Change in momentum/time

= [m (vu)]/t

However, acceleration a = Change in velocity/time = (vu)/t

Therefore, rate of change of momentum = ma = mass × acceleration

This relation holds true when the mass of the body remains constant.

The acceleration produced in a body by a force of given magnitude depends on the following factor:

(a) Size of the body (b) Shape of the body

(c) Mass of the body (d) None of these.

Mass of the body

A force of 10 N acts on a body of mass 5 kg. Find the acceleration produced.

Force, F = 10 N

Mass, m = 5kg

Acceleration, a = F/m [ From Newton's second law]

Or, a = (10/5) ms^{-2}

Or, a = 2 ms^{-2}

Two bodies *A *and *B *of same mass are moving with velocities *v *and *2v, *respectively. Compare their (i) inertia and (ii) momentum.

(i) Mass is the measure of inertia.

Let 'm' be the mass of the two bodies.

Inertia of body A:Inertia of body B :: m:m

Or, Inertia of body A:Inertia of body B :: 1:1

(ii) Momentum of body A = m (v)

Momentum of body B = m (2v) = 2mv

Momentum of body A:Momentum of body B :: mv:2mv

Or, Momentum of body A:Momentum of body B :: 1:2.

Calculate the magnitude of force which when applied on a body of mass 0.5 kg produces an acceleration of 5 m s^{-2}.

Mass, m = 0.5 kg.

Acceleration, a = 5 ms^{-2}

Force, F = ma [ From Newton's second law]

Or, F = (0.5) (5) N = 2.5 N.

Two balls *A *and *B *of masses *m *and 2 *m *are in motion with velocities *2v *and *v, *respectively. Compare:

(i) Their inertia.

(ii) Their momentum.

(iii) The force needed to stop them in the same time.

(i) Inertia of body A:Inertia of body B :: m:2m

Or, Inertia of body A:Inertia of body B :: 1:2.

(ii) Momentum of body A = m ( 2v) = 2mv

Momentum of body B = (2m) v = 2mv

Momentum of body A:Momentum of body B :: 2 mv:2mv

Or, Momentum of body A:Momentum of body B :: 1:1.

(iii) According to Newton's 2^{nd} law of motion, rate of change of momentum is directly proportional to the force applied on it. Therefore,

Force needed to stop A:Force needed to stop B :: 1:1.

A force of 10 N acts on a body of mass 2 kg for 3 s, initially at rest. Calculate: (i) The velocity acquired by the body and (ii) Change in momentum of the body.

Force, F = 10 N

Mass, m = 2 kg

Time, t = 3 s

Initial velocity, u = 0 m/s.

(i) Let v be the final velocity acquired.

From Newton's second law,

F = ma.

Or, a = F/m = 10/2 = 5 ms^{-2}.

From the 1^{st} equation of motion,

a = (vu)/t

Or, v = at + u.

Or, v = (5)(3) + 0 = 15 m/s^{-1}

(ii) Change in momentum = Final momentum initial momentum

p = mv mu.

Or, p = m (vu).

Or, p = 2 ( 15 0) = 30 kg m/s^{-1}

State the Newton's second law of motion. What information do you get from it?

According to Newton's second law of motion, the rate of change of momentum is directly proportional to the force applied on it and the change of momentum takes place in the direction in which the force is applied.

It gives the quantitative value of force, i.e. it relates the force to the measurable quantities such as acceleration and mass.

A force acts for 10 s on a stationary body of mass 100 kg, after which the force ceases to act. The body moves through a distance of 100 m in the next 5 s. Calculate: (i) The velocity acquired by the body, (ii) The acceleration produced by the force and (iii) The magnitude of the force.

Mass, m = 100 kg

Distance moved, s = 100 m

Initial velocity, u = 0

(i) Because the body moves through a distance of 100 m in 5 s,

Velocity of the body = Distance moved / time taken

Velocity = (100/5) = 20 m/s^{-1}

(ii) From Newton's third equation of motion,

v^{2 } u^{2} = 2as.

Or, a = (v^{2 } u^{2}) /2s.

Or, a = [ (20^{2} 0^{2})/ 2(100) ] ms^{-2}.

Or, a = 2 ms^{-2}.

(iii) Force, F = ma

Or, F = (100) (2) N.

Or, F = 200 N.

How does Newton's second law of motion differ from the first law of motion?

Newton's first law of motion gives the qualitative definition of force. It explains the force as the cause of acceleration only qualitatively but Newton's second law of motion gives the quantitative value of force. It states force as the product of mass and acceleration. Thus, it relates force to the measurable quantities such as acceleration and mass.

Fig. shows the velocity-time graph of a particle of mass 100 g moving in a straight line. Calculate the force acting on the particle.

(Hint : Acceleration = Slope of the *v*-*t *graph)

Slope of a velocity-time graph gives the value of acceleration.

Here, slope = 20/5 = 4 m/s^{2}.

Or, acceleration, a = 4 m/s^{2}.

Force = Mass × Acceleration.

Given mass, m = 100 g = 0.1 kg.

Force = (0.1) (4) = 0.4 N.

Write the mathematical form of Newton's second law of motion. State the conditions if any.

Mathematical expression of Newton's second law of motion is as shown below:

Force = Mass × Acceleration

Above relation holds for the following conditions:

(i) When the velocity of the body is much smaller than the velocity of light.

(ii) When the mass remains constant.

A force causes an acceleration of 10 m s^{-2} in a body of mass 500 g. What acceleration will be caused by the same force in a body of mass 5 kg?

Let the force be F.

Force F causes an acceleration, a = 10 m/s^{2} in a body of mass, m = 500 g or 0.5 kg

Thus, F = ma

Or, F = (0.5) (10) = 5 N

Let a' be the acceleration which force F (=5N) cause on a body of mass, m' = 5 kg.

Then, a' = F/m'.

Or, a' = (5/5) ms^{-2}.

Or, a' = 1 ms^{-2}.

State Newton's second law of motion. Under what condition does it take the form F* *= ma?

According to Newton's second law of motion, the rate of change of momentum is directly proportional to the force applied on it, and the change of momentum takes place in the direction in which the force is applied.

The relation F=ma holds for the following conditions:

(i) When the velocity of the body is much smaller than the velocity of light.

(ii) When the mass remains constant.

A force acts for 0.1 s on a body of mass 2.0 kg initially at rest. The force is then withdrawn and the body moves with a velocity of 2 m s^{-1}. Find the magnitude of the force.

Mass, m = 2 kg

Initial velocity, u = 0

Final velocity, v = 2 m/s

Time, t = 0.1 s

Acceleration = Change in velocity/time

Or, a = (v u) /t

Or, a = (2 0)/ 0.1 = 20 ms^{-2}.

Force = Mass Acceleration

Or, F = (2) (20) = 40 N.

How can Newton's first law of motion be obtained from the second law of motion?

From Newton's second law of motion, F = ma.

If F = 0, then a = 0.

This means that if no force is applied on the body, its acceleration will be zero. If the body is at rest, then it will remain in the state of rest and if it is moving, then it will remain moving in the same direction with the same speed. Thus, a body not acted upon by an external force, does not change its state of rest or motion. This is the statement of Newton's first law of motion.

A body of mass 500 g, initially at rest, is acted upon by a force which causes it to move a distance of 4 m in 2 s, Calculate the force applied.

Thus, the force applied to move the body is 1 Newton.

Draw graphs to show the dependence of (i) acceleration on force for a constant mass and (ii) force on mass for a constant acceleration.

A car of mass 480 kg moving at a speed of 54 km per hour is stopped in 10 s. Calculate the force applied by the brakes.

Mass, m = 480 kg.

Initial velocity, u = 54 km/hr = 15 m/s.

Final velocity, v = 0.

Time, t = 10 s.

Acceleration = Change in velocity/time.

Or, a = (v u)/t.

Or, a = (015)/10 = -1.5 ms^{-2}.

Here, negative sign indicates retardation.

Now, Force = Mass Acceleration

Or, F = (480) (1.5) = 720 N.

How does the acceleration produced by a given force depend on the mass of the body? Draw a graph to show it.

If a given force is applied on bodies of different masses, then the acceleration produced in them is inversely proportional to their masses.

A graph plotted for acceleration (a) against mass (m) is a hyperbola.

A car is moving with a uniform velocity 30 ms^{-1}. It is stopped in 2 s by applying a force of 1500 N through its brakes.

Calculate the following values:

(a) The change in momentum of car.

(b) The retardation produced in car.

(c) The mass of car.

Initial velocity, u = 30 m/s

Final velocity, v = 0

Time, t = 2s

Force, F = 1500 N

Here, a = (v u)/t = (0 30)/ 2 = 15 ms^{-2}. Here, negative sign indicates retardation.

Now, F = ma.

Or, m = F/a = (1500/ 15) = 100 kg.

(a) Change in momentum = Final momentum - Initial momentum

Or, p = m (vu)

Or, p = 100 (0 30)

Or, p = 3000 kg m/s^{-1}

(b) Acceleration, a = (vu)/t.

Or, a = (0 30)/ 2 = 15 ms^{-2},

Here, negative sign indicates retardation.

Thus, retardation = 15 ms^{-2}.

(c) From Newton's second law of motion,

F = ma

Or, m = F/a = (1500/ 15) = 100 kg.

Name the S.I. unit of force and define it.

The S.I. unit of force is newton.

One newton is the force which acts on a body of mass 1kg and produces an acceleration of 1 m/s^{2}, i.e. 1 N = 1 kg × 1 m/s^{2}.

A bullet of mass 50 g moving with an initial velocity 100 m s^{-1} strikes a wooden block and comes to rest after penetrating a distance 2 cm in it. Calculate: (i) Initial momentum of the bullet, (ii) Final momentum of the bullet, (iii) Retardation caused by the wooden block and (iv) Resistive force exerted by the wooden block.

Mass, m = 50 gm = 0.05 kg.

Initial velocity, u = 100 m/s.

Final velocity, v = 0.

Distance, s = 2cm = 0.02 m.

(i) Initial momentum = mu = (0.05) (100) = 5 kg m/s^{-1}

(ii) Final momentum = mv = (0.05) (0) = 0 kg m/s.

(iii) Acceleration, a = (v^{2 } u^{2})/2s.

Or, a = (0^{2} 100^{2})/ 2(0.02).

Or, a = 2.5 10^{5} ms^{-2}.

Therefore, retardation is 2.5 10^{5} ms^{-2}.

(iv) Force, F = ma

Or, F = (0.05 kg) (2.5 10^{5} ms^{-2})

Or, F = 12500 N

What is the C.G.S. unit of force? How is it defined?

The C.G.S. unit of force is dyne.

One dyne is the force which acts on a body of mass 1 gramme and produces an acceleration of 1 cms^{-2}, i.e. 1 dyne = 1 g × 1 cms^{-2}.

Name the S.I. and C.G.S. units of force. How are they related?

The S.I. unit of force is newton and the C.G.S. unit of force is dyne.

1 N = 10^{5} dyne.

Why does a glass vessel break when it falls on a hard floor, but it does not break when it falls on a carpet?

When a glass vessel falls from a height on a hard floor, it comes to rest almost instantaneously, i.e. in a very short time, so the floor exerts a large force on the vessel and it breaks. However, if it falls on a carpet, then the time duration, in which the vessel comes to rest, increases, so the carpet exerts less force on the vessel and it does not break.

Use Newton's second law of* *motion to explain the following instances:

(a) You pull your hands back while catching a fast moving cricket ball.

(b) You prefer to land on sand instead of hard floor while taking a high jump.

(a) We pull our hands back while catching a fast moving cricket ball, because by doing so, we increase the time of catch, i.e. increase the time to bring about a given change in momentum, and hence, the rate of change of momentum decreases. Thus, a small force is exerted on our hands by the ball.

(b) When an athlete lands from a height on a hard floor, his feet comes to rest instantaneously, so a very large force is exerted by the floor on his feet, but if he lands on sand, his feet push the sand for some distance; therefore, the time duration in which his feet comes to rest increases. As a result, the force exerted on his feet decreases and he is saved from getting hurt.

## Chapter 3 - Laws of Motion Exercise Ex 3(D)

State the purpose of Newton's third law of motion.

Newton's third law explains how a force acts on an object.

Newton's third law does which of the following actions:

(a) Defines the force qualitatively. (b) Defines the force quantitatively.

(c) Explains the way the force acts on a body. (d) Gives the direction of force.

Explains the way the force acts on a body.

A boy pushes a wall with a force of 10 N towards east. What force is exerted by the wall on the boy?

The wall exerts an equal force of 10 N on the boy in the opposite direction, i.e. west.

State Newton's third law of motion.

According to Newton's third law of motion, to every action there is always an equal and opposite reaction. The action and reaction act simultaneously on two different bodies.

Action and reaction act on:

(a) Same body in opposite directions.

(b) Different bodies in opposite directions.

(c) Different bodies, but in the same direction.

(d) Same body in the same direction.

Different bodies in opposite directions

In the Fig., a block of weight 15 N is hanging from a rigid support by a string. What force is exerted by (a) a block on the string and (b) a string on the block? Name and show them in the diagram.

(a) A block exerts 15 N force (weight) on the string downwards.

(b) The string exerts an equal force of 15 N on the block in the opposite direction, i.e. upward direction (tension).

State and explain the law of action and reaction. by giving two* *examples.

**Law of action and reaction:** In an interaction of two bodies A and B, the magnitude of action, i.e. the force F_{AB} applied by the body B on the body A, is equal in magnitude to the reaction, i.e., the force F_{BA} applied by the body A on the body B, but they are in directions opposite to each other.

Examples:

(i) When a book is placed on a table, it does not move downwards. It implies that the resultant force on the book is zero, which is possible only if the table exerts an upward force of reaction on the book, equal to the weight of the book.

(ii) While moving on the ground, we exert a force by our feet to push the ground backwards; the ground exerts a force of the same magnitude on our feet forward, which makes it easier for us to move.

Explanation: In the above stated example, there are two objects and two forces. In the first example, the weight of the book acts downwards (action) and the force of the table acts upwards (reaction).

In the second example, our feet exerts a force on the ground (action) and the ground exerts an equal and opposite force (reaction) on our feet.

Name and state the action and reaction in the following cases:

(a) Firing a bullet from a gun, (b) Hammering a nail,

(c) A book lying on a table, (d) A moving rocket,

(e) A person moving on the floor,

(f) A moving train colliding with a stationary train.

(a) Action: Force exerted on the bullet.

Reaction: Recoil experienced by the gun.

(b) Action: The force exerted by the hammer on the nail.

Reaction: The force applied by the nail on the hammer.

(c) Action: Weight of the book acting downwards.

Reaction: Force acted by the table upwards.

(d) Action: Force exerted by the rocket on the gases backwards.

Reaction: Force exerted by outgoing gases on the rocket in forward direction.

(e) Action: Force exerted by the feet on the ground in backward direction.

Reaction: Force exerted by the ground on feet in forward direction.

(f) Action: Force exerted by a moving train on a stationary train.

Reaction: Force exerted by a stationary train on a moving train.

Explain the motion of a rocket with the help of Newton's third law.

When a rocket moves in space, it pushes gases outside, i.e. the rocket applies force on the gases in the backward direction. As a reaction, the gases put equal amount of force on the rocket in the opposite direction and the rocket moves in the forward direction.

When a shot is fired from a gun, the gun is recoiled. Explain.

When a man fires a bullet from a gun, a force F is exerted on the bullet (action), and the gun experiences an equal and opposite recoil (reaction) and hence gets recoiled.

When you step ashore from a stationary boat, it tends to leave the shore. Explain.

When a man exerts a force (action) on the boat by stepping into it, its force of reaction makes him step out of the boat, and the boat tends to leave the shore due to the force exerted by the man (i.e. action).

When two spring balances joined at their free ends are pulled apart, both show the same reading. Explain.

Couple two spring balances A and B as shown in the figure. When we pull the balance B, both the balances show the same reading indicating that both the action and reaction forces are equal and opposite. In this case, the pull of either of the two spring balances can be regarded as action and that of the other balance as the reaction.

To move a boat ahead in water, the boatman has to push the water backwards by his oar. Explain this statement.

To move a boat, the boatman pushes (action) the water backwards with his oar. In this response, the water exerts an equal and opposite force (reaction) in the forward direction on the boat due to which the boat moves ahead.

A person pushing a wall hard is liable to fall backwards. Give reason.

A person pushing a wall hard (action) by his palm, experiences a force (reaction) exerted by the wall on his palm in the opposite direction; thus, he is liable to fall backwards.

The action and reaction both act simultaneously. Is this statement true?

Yes, action and reaction act simultaneously.

'Action and reaction are equal in magnitude'. Is this statement true?

Yes, action and reaction are equal in magnitude.

A light ball falling on ground, after striking the ground rises upwards. Explain the reason.

When a falling ball strikes the ground, it exerts a force on the ground. The ground exerts a force back at the ball in the opposite direction. This is the reason the ball rises upwards.

Comment on the statement 'the sum of action and reaction on a body is zero'.

The given statement is wrong.

Reason: According to Newton's third law of motion, the action and reaction act simultaneously on different bodies. Hence they do not cancel each other.

## Chapter 3 - Laws of Motion Exercise Ex 3(E)

State Newton's law of gravitation.

Newton's law of gravitation: Every particle in the universe attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them, and the direction of the force is along the line joining the masses.

The gravitational force between two bodies has the following property:

(a) Always repulsive

(b) Always attractive

(c) Attractive only at large distances (d) Repulsive only at large distances.

Always attractive

The force of attraction between two bodies at certain separation is 10 N. What will be the force of attraction between them if the separation between them is reduced to half?

Given the force of attraction between two bodies = 10 N

Now, .

If the new distance R'= R/2, then let F' be the force acting between the bodies. Then:

State whether the gravitational force between two masses is attractive or repulsive?

Gravitational force is always attractive.

The value of G is one of the values listed below:

(a) 9.8 N m^{2} kg^{-2}

(b) 6.7 x 10^{-11} N m^{2} kg^{-2} (c) 6.7 x 10^{-11} m s^{-2}

(d) 6.7 N kg^{-1}

6.7 x 10^{-11} N m^{2} kg^{-2}

Write the approximate weight of a body of mass 5 kg. What assumption have you made?

Weight = mg

W = (5) (9.8) = 50 N.

Assumption: Value of acceleration due to gravity = 9.8 m/s^{2}.

Write an expression for the gravitational force of attraction between two bodies of masses m_{1} and m_{2} separated by a distance r.

Here G is a constant of proportionality called the universal gravitational constant.

The force of attraction between two masses each of 1 kg kept at a separation of 1 m is which one of the values shown below:

(a) 9.8 N (b) 6.7 N

(c) 980 N (d) 6.7 x 10^{-11} N

6.7 x 10^{-11} N

Calculate the weight of a body of mass 10 kg in (a) kgf and (b) newton. Take g = 9.8 m s^{-2}.

Mass = 10 kg

(i) Weight (in kgf) = 10 x 1 kgf = 10 kgf

[1 kgf = 9.8 N]

(ii) Weight (in newton) = 10 x 9.8 = 98 N.

How does the gravitational force of attraction between two masses depend on the distance between them?

The gravitational force of attraction between two masses is inversely proportional to the square of distance between them.

A body is projected vertically upward with an initial velocity u. If acceleration due to gravity is g, the time for which it remains in air is given by the following relation:

(a) (b) ug

(c) (d)

METHOD: Let't' be the time in which the body reaches its maximum height.

Initial velocity = u.

Final velocity (at the highest point) = 0.

Acceleration due to gravity = g (negative sign indicates the body is moving against gravity).

Using the first equation of motion,

v = u + gt.

We get,

0 = u gt

Or t = u/g

Now total time for which the ball remains in air = Time of ascent + Time of descent

Because time of ascent = Time of descent,

Total time taken = u/g + u/g = 2u/g

State the magnitude and direction of the force of gravity acting on the body of mass 5 kg. Take g = 9.8 m s^{-2}.

Mass = 5 kg.

g = 9.8 m/s^{2}.

Let F be the force of gravity,

F = mg.

F = (5) (9.8) = 49 N.

Force of gravity always acts downwards.

How is the gravitational force between two masses affected if the separation between them is doubled?

If the distance between the masses becomes half, the force reduces to one-fourth.

An object falling freely from rest reaches ground in 2 s. If acceleration due to gravity is 9.8 m s^{-2}, then the velocity of object on reaching the ground will be as shown below:

(a) 9.8 m s^{-1} (b) 4.9 m s^{-1} (c) 19.6 m s^{-1} (d) Zero.

19.6 m s^{-1}

METHOD: Given, u = 0

g = 9.8 m/s^{2}

Time t = 2s

Let 'v' be the velocity of object on reaching the ground.

Using the first equation of motion,

v = u + gt

We get,

v = 0 + (9.8) (2)

Or, v = 19.6 m/s.

The weight of a body is 2.0 N. What is the mass of the body? (g = 10 m s^{-2})

Weight, W = 2.0 N

g = 9.8 m/s^{2}

Let 'm' be the mass of the body.

W = mg

Or, m = W/g = (2/9.8) kg = 0.2 kg.

Define gravitational constant G.

The gravitational constant is defined as the force of attraction between two bodies of unit mass separated by a unit distance.

The weight of a body on Earth is 98 N, where acceleration due to gravity is 9.8 m s^{-2}. What will be its (a) mass and (b) weight on the Moon, where acceleration due to gravity is 1.6 m s^{-2}?

Weight of the body on Earth = 98 N.

Acceleration due to gravity on Earth = 9.8 m/s^{2}.

Let 'm' be the mass of the body on Earth.

m = W/g

m = (98/9.8) = 10 kg

Thus, the mass of the body is 10 kg, which always remains constant.

(a) Mass on moon = mass on Earth = 10 kg

(b) Let weight on moon is W'.

W' = mass acceleration due to gravity on the Moon.

[Given, acceleration due to gravity on the Moon = 1.6 m/s^{2}]

W' = 10 1.6 =16 N.

Write the numerical value of gravitational constant G with its S.I. unit.

The value of G in the S.I. system is 6.67 x 10^{-11}Nm^{2}kg^{-2}.

A man weighs 600 N on the Earth. What would be his approximate weight on the Moon? Give a reason for your answer?

Man's weight on Earth = 600 N

Man's weight on the Moon = (1/6) man's weight on Earth;

Because the acceleration due to gravity on the Moon is 1/6^{th} that of Earth and w = mg.

Therefore, man's weight on Moon = (600/6) = 100 N.

What is the importance of law of gravitation?

The gravitational force of attraction is significant to explain the motion of heavenly bodies, e.g. motion of planets around the Sun, motion of the Moon around the Earth etc.

What (a) force and (b) weight act on a mass of 10.5 kg being pulled by the Earth? Take g = 10 m s^{-2}.

Mass, m = 10.5 kg

G = 10 m/s^{2}

(a) Force, F = mg

F = (10.5) (10) = 105 N

(b) Weight, w = mg

w = (10.5) (10) = 105 N

What do you understand by the term force due to gravity?

The force with which the Earth attracts a body towards its centre is called the force due to gravity.

A ball is released from a height and it reaches the ground in 3 s. If g= 9.8 m s^{-2}, find the value for the following variables:

(a) The height from which the ball was released.

(b) The velocity with which the ball will strike the ground.

Let 'S' be the height.

Time taken, t = 3s; g = 9.8 m/s^{2}

Initial velocity, u = 0 (because the body starts from rest)

(a) Using the second equation of motion,

S = ut + (1/2) gt^{2}

We get,

S = 0 + (1/2) (9.8) (3) (3)

S = 44.1 m

(b) Let 'v' be the velocity with which the ball strikes the ground.

Using the third equation of motion,

v^{2} u^{2} = 2gs

or, v^{2} - 0^{2} = 2(9.8) (44.1)

or, v^{2} = 864.36

or, v = 29.4 m/s

Write an expression for the force due to gravity on a body of mass m and explain the meaning of symbols used in it.

The force due to gravity on a body of mass m kept on the surface of Earth (mass=M and radius=R) is equal to the force of attraction between the Earth and that body.

What force, in newton, your muscles need to apply to hold a mass of 5 kg in your hand? State the assumption.

Mass, m = 5kg

Force, F = mg

F = (5) (9.8) = 49 N

Assumption: Value of acceleration due to gravity is 9.8 m/s^{2}.

Define the term acceleration due to gravity? Write its S.I. unit.

The rate at which the velocity of a freely falling body increases is called acceleration due to gravity. Its S.I. unit is m/s^{2}.

A ball is thrown vertically upwards. It goes to a height 20 m and then returns to the ground. Taking acceleration due to gravity g to be 10 m s^{-2}, find the following variables:

(a) The initial velocity of the ball

(b) The final velocity of ball on reaching the ground and

(c) The total time of journey of ball.

Given, maximum height reached, s = 20 m

Acceleration due to gravity, g = 10 m/s^{2}

(i) Let 'u' be the initial velocity.

At the highest point, velocity = 0

Using the third equation of motion,

v^{2 } u^{2 }= 2gs

or, 0 u^{2 }= 2 (10) (20) m/s

or, u^{2 }= (400) m/s [Negative sign indicates that the motion is against gravity]

or, u = 20 m/s

(b) Let v' be the final velocity of the ball on reaching the ground.

Considering the motion from the highest point to ground,

Velocity at highest point = 0 = Initial velocity for downward journey of the ball.

Distance travelled, s = 20m

Using the third equation of motion,

v^{2 } u^{2 }= 2gs

or, v^{2 } 0 = 2 (10) (20) m/s

or, v^{2 }= 400 m/s

or, v = 420 m/s

(c) Now total time for which the ball remains in air, t = 2u/g.

Or, t = 2 (20)/(10).

Or, t = 4s.

Write down the average value of g on Earth's surface.

The average value of 'g' on the Earth's surface is 9.8 m/s^{2}.

An object is dropped from the top of a tower. It acquires a velocity 20 m s^{-1} on reaching the ground. Calculate the height of the tower. (Take g = 10 m s^{-2})

Initial velocity u = 0

Final velocity = 20 m/s

g = 10 m/s^{2}

Let 'h' be the height of the tower.

Using the third equation of motion,

v^{2} u^{2} = 2gs

or, (20)^{2} 0 = 2 (10) h

or, h = 20 m

How is the acceleration due to gravity on the Earth's surface related to the mass and radius of the Earth?

Let g be the acceleration due to gravity on the Earth's surface (mass = M and radius = R).

Then,

A ball is thrown vertically upwards. It returns 6 s later. Calculate: (i) The greatest height reached by the ball and (ii) The initial velocity of the ball. (Take g = 10 m s^{-2})

Total time of journey = 6 s

g = 10 m/s^{2}

(i) Let 'H' be the greatest height.

Time of ascent, t = 6/2 = 3 s,

For ascent, initial velocity, u = 0

Using the second equation of motion,

H = ut + (1/2) gt^{2}

H = 0 + (1/2) (10) (3)^{ 2}

H = 45 m

(ii) Let u' be the initial velocity.

Final velocity, v = 0

Using the third equation of motion,

v^{2} u^{2} = 2gH

or, v^{2} 0 = 2(10) (45)

or, v^{2} = 900

or, v = 30 m/s

How are g and G related?

Acceleration due to gravity (g) is directly proportional to universal gravitational constant (G).

A pebble is thrown vertically upwards with a speed of 20 m s^{-1}. How high will it be after 2 s? (Take g = 10 m s^{-2})

Initial velocity, u = 20 m/s

Time, t = 2s

g = 10 m/s^{2}

Maximum height reached in 2s, H = (1/2) gt^{2}

Or, H = (1/2) (10) (2)^{ 2}

Or, H = 20 m

A body falls freely under gravity from rest and reaches the ground in time t. Write the expression for the height fallen by the body.

Initial velocity, u = 0.

Time taken = t.

Acceleration due to gravity = g.

Let 'h' be the height fallen.

(a) How long will a stone take to fall to the ground from the top of a building 80 m high and (b) What will be the velocity of the stone on reaching the ground? (Take g=10 m s^{-2})

(a) Height, s = 80m

g = 10 m/s^{2}

Using the second equation of motion,

S = ut + (1/2) gt^{2}

Or, 80 = 0+ (1/2) (10) (t)^{ 2}

Or, (t)^{ 2} = 16

Or, t = 4s

(b) Let 'v' be the velocity on reaching the ground.

Using the third equation of motion,

v^{2} u^{2} = 2gH

or, v^{2} 0 = 2(10) (80)

or, v^{2} = 1600

or, v = 40 m/s

A body is thrown vertically upwards with an initial velocity u. Write the expression for the maximum height attained by the body.

If a body is thrown vertically up with an initial velocity u to a height h, then there will be retardation (a = g).

At the highest point, the final velocity v = 0.

Thus, from the third equation,

A body falls from the top of a building and reaches the ground 2.5 s later. How high is the building? (Take g = 9.8 m s^{-2})

Given time t = 2.5, g = 9.8 m/s^{2}

Height, H = (1/2) gt^{2}

Or, H = (1/2) (9.8) (2.5)^{2}

Or, H = 30.6 m

Define the terms mass and weight.

Mass: The mass of a body is the quantity of matter it contains.

Weight: The weight of a body is the force with which the Earth attracts it.

A ball is thrown vertically upwards with an initial velocity of 49 m s^{-1}. Calculate: (i) The maximum height attained, (ii) The time taken by it before it reaches the ground again. (Take g = 9.8 m s^{-2}).

Initial velocity, u = 49 m/s

g = 9.8 m/s^{2}

(i) Let H be the maximum height attained.

At the highest point, velocity = 0.

Using the third equation of motion,

v^{2} u^{2} = 2gH

or,0 49^{2} = 2(9.8) (H)

or, H = (49^{2})/ 19.6

or, H = 122.5 m

(ii) Total time of flight is given by t = 2u/g

Or, t = 2(49)/ 9.8

Or, t = 10 s

Distinguish between mass and weight.

Mass is a scalar quantity, but weight is a vector quantity. Mass is the measure of the quantity of matter contained in a body, but weight is the measure of force with which the Earth attracts the body. Mass of a body is always constant but weight varies from place to place.

A stone is dropped freely from the top of a tower and it reaches the ground in 4 s. Taking g = 10m s^{-2}, calculate the height of the tower.

Initial velocity u = 0

Time t = 4 s

g = 10 m/s^{2}

Let 'H' be the height of the tower.

Using the second equation of motion,

H = ut + (1/2) gt^{2}

Or, H = 0 + (1/2)(10)(4)^{2}

Or, H = 80 m

State the S.I. units of (a) mass and (b) weight.

The S.I. unit of mass is kg and that of weight is newton.

A pebble is dropped freely in a well from its top. It takes 20 s for the pebble to reach the water surface in the well. Taking g = 10 m s^{-2} and speed of sound = 330 m s^{-1}. Find: (i) The depth of water surface and (ii) The time when echo is heard after the pebble is dropped.

(i) Time t =20 s

g = 10 m/s^{2}

Let 'D' be the depth of the well.

Using the second equation of motion,

D = ut + (1/2) gt^{2}

D = 0 + (1/2)(10)(20)^{ 2}

D = 2000 m

(ii) Speed of sound = 330 m/s

Depth of well = 2000 m

Time taken to hear the echo after the pebble reaches the water surface = Depth/speed

= (2000/330) s

= 6.1 s

Time taken for pebble to reach the water surface = 20 s.

Therefore, the total time taken to hear the echo after the pebble is dropped = 20 + 6.1 = 21.6 s.

The value of g at the centre of Earth is zero. What will be the weight of a body of mass m kg at the centre of the Earth?

W = mg

At the centre of Earth, g = 0.

Therefore, W = 0.

A ball is thrown vertically upwards from the top of a tower with an initial velocity of 19.6 m s^{-1}. The ball reaches the ground after 5 s. Calculate: (i) The height of the tower, (ii) The velocity of the ball on reaching the ground. Take g= 9.8 ms^{-2}.

Let x be the height of the tower.

Let h be the distance from the top of the tower to the highest point as shown in the diagram.

Initial velocity u = 19.6 m/s

g = 9.8 m/s^{2}

At the highest point, velocity = 0

Using the third equation of motion,

v^{2} u^{2} = 2gh

Or, (19.6)^{ 2} = 2 (9.8) h

Or, h = 19.6 m

If the ball takes time t_{1} to go to the highest point from the top of building, then for the upward journey from the relation, v = u gt,

0 = 19.6 (9.8) (t_{1})

Or, t_{1} = 2s

(ii) Let us consider the motion for the part (x+h)

Time taken to travel from highest point to the ground = (5 2) = 3s

Using the equation s = ut + (1/2) gt^{2}

We get,

(x + h) = 0 + (1/2) (9.8) (3)^{ 2}

Or, (x + 19.6) = 44.1 m

Or, x = 44.1 19.6 = 24.5 m

Thus, height of the tower = 24.5 m

(iii) Let v be the velocity of the ball on reaching the ground.

Using the relation, v = u + gt

We get:

v = 0 + (9.8) (3)

Or, v = 29.4 m/s

Which of the quantity is constant for a body: mass or weight?

Mass of a body is always constant.

Explain the meaning of the following statement '1 kgf = 9.8 N'.

1 kgf = 9.8 N.

One kilogramme force is the force due to gravity on a mass of 1 kilogramme.

## Chapter 3 - Laws of Motion Exercise Ex 3(A)

Explain giving two examples each of :

a. Contact forces

b. Non - contact forces

a. The forces which act on bodies when they are in physical contact are called contact forces.

Example: frictional force and force exerted on two bodies during collision.

b. The forces experienced by bodies even without being physically touched are called non-contact forces.

Example: Gravitational force and Electrostatic force.

Which of the following is a contact force:

a. Electrostatic force

b. Gravitational force

c. Frictional force

d. Magnetic force

Frictional force is a contact force.

Classify the following amongst contact and non - contact forces:

a. Frictional force

b. Normal reaction force

c. Force of tension in a string

d. Gravitational force

e. Electrostatic force

f. Magnetic force

Contact force: (a) frictional force (b) normal reaction force (c) force of tension in a string

Non-contact force: (d) gravitational force (e) electric force (f) magnetic force

The non - contact force is :

a. Force of reaction

b. Force due to gravity

c. Tension in string

d. Force of friction

Force due to gravity is a non-contact force.

Give one example in each case where :

a. The force is of contact, and

b. Force is at a distance

a. Force exerted on two bodies during collision.

b. Magnetic force between magnetic poles.

A. A ball is hanging by string from the ceiling of the roof. Draw a neat labelled diagram showing the forces acting on the ball and the string.

B. A spring is compressed against a rigid wall. Draw a neat and labeled diagram showing the forces acting on the spring.

C. A wooden block is placed on a table top. Name the forces acting on the block and draw a neat and labelled diagram to show the point of application and direction of these forces.

A.

B.

C.

The forces acting on the block are its weight in the downward direction and the normal reaction force due to the table on the upward direction.

State one factor on which the magnitude of a non-contact force depends. How does it depend on the factor stated by you?

The magnitude of non-contact force on two bodies depends on the distance of separation between them.

The force decreases as the distance of separation increases.

The force is inversely proportional to the square of the distance of separation.

The separation between two masses is reduced to half. How is the magnitude of gravitational force between them affected?

The magnitude of gravitational force between two masses will become four times as gravitational force varies inversely as the square of distance of separation.

State the effects of a force applied on

i. A non-rigid, and

ii. A rigid body.

How does the effect of the force differ in the two cases?

A force when applied on a non-rigid body changes the inter-spacing between its constituent particles and therefore causes a change in its dimensions and can also produce motion in it.

On the other hand, a force when applied on a rigid body, does not change the inter-spacing between its constituent particles and therefore it does not change the dimensions of the body but causes motion in it

Give one example in each of the following cases where a force:

i. Stops a moving body.

ii. Moves a stationary body.

iii. Changes the size of a body.

iv. Changes the shape of a body.

- A fielder on the ground stops a moving ball by applying a force with his hands.
- The pull exerted by horse makes a cart moves.
- In a cycle pump, when the piston is lowered, the air is compressed to occupy a less volume.
- On pressing a piece of rubber, its shape changes.

## Chapter 3 - Laws of Motion Exercise Ex 3(B)

Name the physical quantity that causes motion in a body.

Force causes motion in a body.

The property of inertia is more in the following vehicle:

(a) A car (b) A truck

(c) A horse cart (d) A toy car.

A truck

Is force needed to keep a moving body in motion?

Force is not needed to keep a moving body in motion.

A tennis ball and cricket ball are both stationary. To get them into the state of motion, the following action is required:

(a) Less force is required for the cricket ball than for the tennis ball.

(b) Less force is required for the tennis ball than for the cricket ball.

(c) Same force is required for both the balls.

(d) Nothing can be said.

Less force is required for the tennis ball than for the cricket ball.

A ball moving on a table eventually stops. Explain the reason.

The force of friction between the table and the ball opposes the motion of the ball.

A force is needed to do the following actions:

(a) Change the state of motion or state of rest of the body.

(b) Maintain the body in motion. (c) Maintain the body at rest.

(d) Maintain constant velocity of the body.

Change the state of motion or state of rest of the body.

A ball is moving on a perfectly smooth horizontal surface. If no force is applied on it, then will its speed decrease, increase or remain unchanged?

In absence of any external force, its speed shall remain unchanged.

What is Galileo's law of inertia?

Galileo's law of inertia states that a body continues to be in its state of rest or of uniform motion unless an external force is applied on it.

State Newton's first law of motion.

According to Newton's first law of motion, if a body is in a state of rest, it will remain in the state of rest, and if the body is in the state of motion, it will remain moving in the same direction with the same speed unless an external force is applied on it.

State and explain the law of inertia (or Newton's first law of motion).

Statement of Newton's first law: If a body is in a state of rest, it will remain in the state of rest, and if the body is in the state of motion, it will remain moving in the same direction with the same speed unless an external force is applied on it.

Explanation: Newton's first law can be explained in the following two parts:

(i) Definition of inertia: The 1^{st} part of Newton's first law of motion gives the definition of inertia, according to which an object cannot change its state by itself.

Example: A book lying on a table will remain in its position unless it is displaced.

(ii) Definition of force: The 2^{nd} part of Newton's first law defines force, according to which force is that external cause which can move a stationary object or which can stop a moving object.

Example: A book lying on a table is displaced from its place when it is pushed.

What is meant by the term inertia?

The property of an object by virtue of which it neither changes its state nor tends to change the state is called inertia.

Give the qualitative definition of force based on Newton's first law of motion.

Force is that external cause which can move a stationary object or which can stop a moving object.

Name the factor on which the inertia of a body depends and state how does it depend on the factor stated above.

Inertia of a body depends on its mass. Inertia is directly proportional to mass, i.e. greater the mass of a body, greater is its inertia.

Give two* *examples to show that greater the mass, greater is the inertia of the body.

Examples to show that greater the mass, greater is the inertia of the body are as shown below:

(i) If you want to start a car by pushing it, you find that it takes a very large force to overcome its inertia. On the other hand, only a small force is needed to start a child's express wagon. The difference between the car and express wagon is the difference in mass. The car has a large mass, whereas the wagon has a small one.

(ii) A cricket ball is more massive than a tennis ball. The cricket ball acquires a much smaller velocity than a tennis ball when the two balls are pushed with equal force for the same time.

'More the mass, the more difficult it is to move the body from rest'. Explain this statement by giving an example.

It is difficult, i.e. a larger force is required to set a loaded trolley (which has more mass) in motion than an unloaded trolley (which has less mass).

Name the two* *kinds of inertia.

Two kinds of inertia are as listed below:

(i) Inertia of rest.

(ii) Inertia of motion.

Give one* *example of each of the following cases of inertia:

(a) Inertia of rest, and

(b) Inertia of motion.

Examples of inertia of rest: A coin placed on top of a card remains in place when the card is slightly and quickly jerked horizontally.

Example of inertia of motion: A ball thrown vertically upwards by a person in a moving train comes back to his hand.

Two equal and opposite forces act on a stationary body. Will the body move? Give a reason to your answer.

No, the body will not move because the net force acting on it is zero. Hence, it will remain stationary due to inertia of rest.

Two equal and opposite forces act on a moving object. How is its motion affected? Give reason.

The motion remains unaffected because the net force acting on it is zero.

An aeroplane is moving uniformly at a constant height under the action of two forces (i) Upward force (lift) and (ii) Downward force (weight). What is the net force on the aeroplane?

The net force on the airplane is zero or the upward force is equal to the downward force.

Why does a person tend to fall when he jumps out from a moving train and tries to stop immediately?

If a person jumps out of a moving train and tries to stop immediately, he falls due to inertia of motion. This is because his body tends to move forward with the velocity of the train while his feet are stationary.

Why does a coin, placed on a card, drop into the tumbler when the card is rapidly flicked with a finger?

The reason is that when the card is flicked, a momentary force acts on the card, so it moves away. However, the coin kept on it does not share the motion at once and it remains stationary at its place due to the inertia of rest. The coin then falls down into the tumbler due to the pull of gravity.

When a ball is thrown vertically upwards from a moving train it comes back to the thrower's hand. Why does this happen?

The reason is that when the ball is thrown, the ball is in motion along with the person and train. Due to the inertia of motion, during the time the ball remains in air, the person and ball move ahead by the same distance. This makes the ball fall back into the thrower's hand.

Explain the following:

(a) When a train suddenly moves forward, the passenger standing in the compartment tends to fall backwards.

(b) When a train suddenly starts, the sliding doors of some compartments may open.

(c) People often shake branches of a tree in an attempt to cause the fruits to fall.

(d) After alighting from a moving bus, one has to run for some distance in the direction of bus in order to avoid falling.

(e) Dust particles are removed from a carpet by beating it.

(f) It is advantageous to run before taking a long jump.

(a) When a train suddenly starts, the passengers tend to fall backwards. This is because the lower part of the body, which is in contact with the train, begins to move while the upper part of the body tends to maintain its position of rest. As a result, the upper part tends to fall backwards.

(b) The frame of the sliding door being in contact with the floor of the train also comes in motion on start of the train, but the sliding door remains in its position due to inertia. Thus, the frame moves ahead with the train, while the door slides opposite to the direction of motion of the train. Thus, the door may shut or open accordingly.

(c) When the branches of the tree are shaken, they come in motion, while the fruits due to inertia remain in a state of rest. Thus, the larger and weakly attached fruits get detached from the branches and fall down due to the pull of gravity.

(d) When people alight from a moving bus, they continue to run alongside the bus to avoid falling. If they were to stop at once, the feet would come to rest suddenly but the upper part of the body would still be in motion and they would tend to fall forward.

(e) The part of the carpet where the stick strikes comes in motion at once, while the dust particles settled on it remain in the state of rest due to inertia of rest. Thus, a part of the carpet moves ahead with the stick leaving behind the dust particles that fall down due to gravity.

(f) When running, the athlete brings his body in the state of motion. When the body is in motion, it becomes easier to take a long jump.

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