NCERT Solutions - Chapter 8: Force and Laws of Motion

Q1. Which of the following has more inertia:
(a) a rubber ball and a stone of the same size?
(b) a bicycle and a train?
(c) a five-rupees coin and a one-rupee coin?

Answer -

Case	Object with More Inertia	Reason
(a) Rubber ball vs Stone (same size)	Stone	Stone has more mass than a rubber ball.
(b) Bicycle vs Train	Train	Train has much greater mass than a bicycle.
(c) ₹5 coin vs ₹1 coin	₹5 coin	₹5 coin is heavier and hence has more inertia.

Q2. In the following example, try to identify the number of times the velocity of the ball changes:
“A football player kicks a football to another player of his team who kicks the football towards the goal. The goalkeeper of the opposite team collects the football and kicks it towards a player of his own team”.
Also identify the agent supplying the force in each case.

Answer - The velocity of the ball changes three times:
1. First player kicks the ball → Velocity changes (Agent: First player)
2. Second player kicks towards the goal → Velocity changes (Agent: Second player)
3. Goalkeeper kicks towards his teammate → Velocity changes (Agent: Goalkeeper)

Q3. Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.

Answer - When we shake a branch vigorously, the branch comes in motion but the leaves tend to stay at rest due to inertia. As a result, the leaves get detached from the branch.

Q4. Why do you fall in the forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest?

Answer - When the bus stops suddenly, your lower body comes to rest with the bus, but your upper body continues moving due to inertia, making you fall forward.
When the bus starts suddenly, the lower body moves with the bus, but the upper body resists motion due to inertia, making you fall backward.

Q1. An object experiences a net zero external unbalanced force. Is it possible for the object to be travelling with a non-zero velocity? If yes, state the conditions that must be placed on it.

Answer - Yes, it is possible for an object to travel with a non-zero velocity if the net external unbalanced force acting on it is zero. This means the object is moving with constant velocity in a straight line, i.e., it is in uniform motion.

Q2. When a carpet is beaten with a stick, dust comes out of it. Explain.

Answer - When we beat a carpet with a stick, the carpet suddenly stops moving due to its inertia. However, the dust particles on the carpet tend to keep moving due to their inertia and thus get separated from the carpet, coming out.

Q3. Why is it advised to tie any luggage kept on the roof of a bus with a rope?

Answer - We tie the luggage on the roof of a bus with a rope because of inertia. When the bus moves or stops suddenly, the luggage tends to keep moving in the same direction due to inertia. The rope holds it firmly and prevents it from falling.

Q4. A batsman hits a cricket ball which then rolls on a level ground. After covering a short distance, the ball comes to rest. The ball slows to a stop because: (a) the batsman did not hit the ball hard enough. (b) velocity is proportional to the force exerted on the ball. (c) there is a force on the ball opposing the motion. (d) there is no unbalanced force on the ball, so the ball would want to come to rest.

Answer - The correct reason is (c) there is a force on the ball opposing the motion. This force is friction between the ball and the ground, which slows the ball down and eventually stops it.

Q5. A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of 400 m in 20 s. Find its acceleration. Find the force acting on it if its mass is 7 tonnes (Hint: 1 tonne = 1000 kg).

Answer - Using the equation s = ut + (1/2)at², where u = 0, s = 400 m, t = 20 s, we get: 400 = 0 + (1/2)a(20)² → 400 = 200a → a = 2 m/s². The acceleration is 2 m/s². The mass of the truck is 7 tonnes = 7000 kg. Force F = mass × acceleration = 7000 × 2 = 14000 N.

Q6. A stone of 1 kg is thrown with a velocity of 20 m s–1 across the frozen surface of a lake and comes to rest after travelling a distance of 50 m. What is the force of friction between the stone and the ice?

Answer - Given:
Mass, m = 1 kg
Initial Velocity, u = 20 m/s
Final Velocity, v = 0 m/s (as object comes to rest)
Distance, s = 50 m

Using the equation: v² = u² + 2as
0 = (20)² + 2 × a × 50
=> 0 = 400 + 100a
=> a = -4 m/s²

F = m × a = 1 × (-4) = -4 N

The force of friction is 4 N, opposite to motion.

Q7. A 8000 kg engine pulls a train of 5 wagons, each of 2000 kg, along a horizontal track. If the engine exerts a force of 40000 N and the track offers a friction force of 5000 N, then calculate:
(a) the net accelerating force and
(b) the acceleration of the train.

Answer - Given:
Mass of engine = 8000 kg
Mass of each wagon = 2000 kg
Number of wagons = 5
Total mass of train = 8000 + (5 × 2000) = 18000 kg
Force exerted by engine = 40000 N
Friction force = 5000 N

(a) Net accelerating force = 40000 − 5000 = 35000 N
(b) Acceleration, a = F / m = 35000 / 18000
=> a ≈ 1.94 m/s²

Q8. An automobile vehicle has a mass of 1500 kg. What must be the force between the vehicle and road if the vehicle is to be stopped with a negative acceleration of 1.7 m s–2?

Answer - Given:
Mass, m = 1500 kg
Acceleration, a = -1.7 m/s²

F = m × a = 1500 × (-1.7)
=> F = -2550 N

The required force is 2550 N opposite to the direction of motion.

Q9. What is the momentum of an object of mass m, moving with a velocity v?
(a) (mv)²
(b) mv²
(c) ½ mv²
(d) mv

Answer - Momentum = mass × velocity = mv

Correct option: (d) mv

Q10. Using a horizontal force of 200 N, we intend to move a wooden cabinet across a floor at a constant velocity. What is the friction force that will be exerted on the cabinet?

Answer - Since the cabinet moves with constant velocity, the net force acting on it is zero.

Friction force = Applied force = 200 N

Q11. According to the third law of motion when we push on an object, the object pushes back on us with an equal and opposite force. If the object is a massive truck parked along the roadside, it will probably not move. A student justifies this by answering that the two opposite and equal forces cancel each other. Comment on this logic and explain why the truck does not move.

Answer - The student’s logic is incorrect. According to Newton’s third law, the two forces act on different bodies, not on the same body, so they do not cancel each other. When we push the truck, our body exerts a force on the truck, and the truck exerts an equal and opposite force on us. The reason the truck does not move is that the force we apply is not large enough to overcome the truck’s inertia and the friction between its tyres and the road.

Q12. A hockey ball of mass 200 g travelling at 10 m/s is struck by a hockey stick so as to return it along its original path with a velocity of 5 m/s. Calculate the magnitude of change of momentum occurred in the motion of the hockey ball by the force applied by the hockey stick.

Answer - Given:
Mass, m = 200 g = 0.2 kg
Initial velocity, u = 10 m/s
Final velocity, v = -5 m/s (opposite direction)

Change in momentum = mv - mu
= 0.2 × (-5) - 0.2 × 10
= -1 - 2 = -3 kg·m/s

Magnitude of change in momentum = 3 kg·m/s

Q13. A bullet of mass 10 g travelling horizontally with a velocity of 150 m/s strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet.

Answer - Given:
Mass, m = 10 g = 0.01 kg
Initial velocity, u = 150 m/s
Final velocity, v = 0 m/s
Time, t = 0.03 s

Using a = (v - u)/t
a = (0 - 150)/0.03 => a = -5000 m/s²

Using s = ut + (1/2)at²
s = 150 × 0.03 + 0.5 × (-5000) × (0.03)²
s = 4.5 - 2.25 = 2.25 m

Force, F = m × a = 0.01 × 5000 = 50 N

Distance of penetration = 2.25 m
Magnitude of force = 50 N

Q14. An object of mass 1 kg travelling in a straight line with a velocity of 10 m/s collides with, and sticks to, a stationary wooden block of mass 5 kg. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object.

Answer - Given:
Mass of object, m₁ = 1 kg
Velocity of object, u₁ = 10 m/s
Mass of block, m₂ = 5 kg
Velocity of block, u₂ = 0 m/s

Total momentum before impact = m₁u₁ + m₂u₂ = 1 × 10 + 5 × 0 = 10 kg·m/s

Let v be the velocity after collision.
Total mass = m₁ + m₂ = 6 kg
Total momentum after impact = (m₁ + m₂)v = 6v

By conservation of momentum:
10 = 6v => v = 10 / 6 = 1.67 m/s

Total momentum before impact = 10 kg·m/s
Total momentum after impact = 10 kg·m/s
Velocity of the combined object = 1.67 m/s

Q15. An object of mass 100 kg is accelerated uniformly from a velocity of 5 m/s to 8 m/s in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.

Answer - Given:
Mass, m = 100 kg
Initial velocity, u = 5 m/s
Final velocity, v = 8 m/s
Time, t = 6 s

Initial momentum = m × u = 100 × 5 = 500 kg·m/s
Final momentum = m × v = 100 × 8 = 800 kg·m/s

Change in momentum = 800 - 500 = 300 kg·m/s

Force, F = (change in momentum) / time
F = 300 / 6 = 50 N

Initial momentum = 500 kg·m/s
Final momentum = 800 kg·m/s
Force exerted = 50 N

Q16. Akhtar, Kiran and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran started pondering over the situation. Kiran suggested that the insect suffered a greater change in momentum as compared to the change in momentum of the motorcar (because the change in the velocity of the insect was much more than that of the motorcar). Akhtar said that since the motorcar was moving with a larger velocity, it exerted a larger force on the insect. And as a result the insect died. Rahul while putting an entirely new explanation said that both the motorcar and the insect experienced the same force and a change in their momentum. Comment on these suggestions.

Answer - Rahul is correct. According to Newton’s third law of motion, the force exerted by the motorcar on the insect and the force exerted by the insect on the motorcar are equal in magnitude and opposite in direction.

Also, according to Newton’s second law, the change in momentum (Δp) is given by force × time. Since both the insect and motorcar experience the same force for the same time, the magnitude of change in momentum is also the same.

However, due to the large mass of the motorcar, the effect of this change (i.e., change in velocity) is negligible. In contrast, the insect has a very small mass, so the same change in momentum results in a large change in its velocity, which causes its death.

Q17. How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 m/s².

Answer - Given:
Mass, m = 10 kg
Height, h = 80 cm = 0.8 m
Acceleration due to gravity, g = 10 m/s²

Using v² = u² + 2gh, where u = 0
v² = 0 + 2 × 10 × 0.8 = 16
=> v = √16 = 4 m/s

Momentum transferred to the floor = m × v = 10 × 4 = 40 kg·m/s