Chapter 9: Force and Laws of Motion

There are three solids made up of aluminium, steel and wood, of the same shape and same volume. Which of them would have highest inertia?

Soln:

Inertia depends on the mass of the object. For the solids with the same size and volume, inertia is determined by its mass. Hence steel will have the highest inertia.

10. Two balls of the same size but of different materials, rubber and iron are kept on the smooth floor of a moving train. The brakes are applied suddenly to stop the train. Will the balls start rolling? If so, in which direction? Will they move with the same speed? Give reasons for your answer.

Soln:

Yes, the balls start rolling in the direction of the train’s movement. When brakes are applied, the train will come to rest and balls try to attain rest because of inertia balls remain in motion and they begin to roll. Since the mass between two balls is not the same, the inertia of the iron ball is greater than the inertia of the rubber ball. Hence, rubber ball rolls faster than the iron ball.

11. Two identical bullets are fired one by a light rifle and another by a heavy rifle with the same force. Which rifle will hurt the shoulder more and why?

Soln:

The momentum of the bullet depends on the backward momentum of the rifle. As per Newton’s third law of motion: recoil velocity is equivalent to the bullet’s velocity, making it lighter. Since the momentum of the lighter rifle is more than the heavier rifle, the bullet fired from lighter rifle hurts the shoulder more.

12. A horse continues to apply a force in order to move a cart with a constant speed. Explain why?

Soln:

When cart moves on the road it has to encounter friction. In order to keep the cart moving horse should overcome the friction. Hence it continues to apply the force.

13. Suppose a ball of mass m is thrown vertically upward with an initial speed v, its speed decreases continuously till it becomes zero. Thereafter, the ball begins to fall downward and attains the speed v again before striking the ground. It implies that the magnitude of initial and final momentums of the ball are same. Yet, it is not an example of conservation of momentum. Explain why?

Soln:

If the external force did not act on the system, the momentum of that system remains constant. In the given case, change in velocity is due to the gravitational force of the earth and hence is not an example of conservation of momentum.

14. Velocity versus time graph of a ball of mass 50 g rolling on a concrete floor is shown in Fig. 9.1. Calculate the acceleration and frictional force of the floor on the ball.

Soln:

Given, m = 50g

F =?

Force = mass × acceleration

= 

velocity = 80ms^-1

Velocity decelerates due to the friction of the floor with itself and comes to rest after 8 seconds.

a = 

= -10m/s²

The negative sign indicates that the frictional force exerted opposes the motion of the ball. Now, using Newton’s relation,

Force = mass× acceleration

= 

= -0.5 N

15. A truck of mass M is moved under a force F. If the truck is then loaded with an object equal to the mass of the truck and the driving force is halved, then how does the acceleration change?

Soln:

Force = mass x acceleration

F=ma

a= f/m

When mass is doubled force is halved m becomes 2m and f becomes f/2

a₂=f/4m or a₂/a₁ = f/4m + f/4m = 1/4

acceleration reduces to

16. Two friends on roller-skates are standing 5 m apart facing each other. One of them throws a ball of 2 kg towards the other, who catches it, How will this activity affect the position of the two? Explain your answer.

Soln:

Distance between them will increase. Before throwing the ball, the momentum of both of them will be zero. To conserve the momentum, the person who throws the ball moves backwards. The person who catches the ball experiences a net force while catching the ball and he moves backwards.

17. Water sprinkler used for grass lawns begins to rotate as soon as the water is supplied. Explain the principle on which it works.

Soln:

Water sprinkler works on the third law of motion. When water comes out of sprinkler an equal and opposite force is exerted. This will cause the sprinkler to rotate.