Question

Why is it easier to catch a tennis ball as compared to a cricket ball moving with the same velocity?

Answer 1

Hint: We know that the mass of a tennis ball is less than a cricket ball. Ease of catching a ball is dependent on the impact/impulse of the ball. This means that the change in the momentum if is low then then it’ll be easier. The momentum of the cricket ball is much higher because of its greater mass.

Complete step by step answer:
Momentum (p):
It is defined as a product of mass and velocity. When an object of mass ‘m’ is moving with velocity ‘v’ then momentum ‘p’ acquired by it is given by
$p = mv$ … (1)
The quantity of motion possessed by a moving body is termed as momentum.
According to Newton’s Second law of motion, the rate of change of momentum gives rise to force. Mathematically;
$\dfrac{{dp}}{{dt}} = F$ … (2)
As we know that the mass of a tennis ball is less compared to a cricket ball. Mass is directly proportional to momentum, according to equation 1. Momentum of the cricket ball will be more than the tennis ball.
When a ball is thrown in air, the momentum of the ball will change with time. Rate of change of momentum will give rise to force as mentioned in equation 2. Tennis ball will strike the catcher with less force and a cricket ball will exert more force. This makes it easier to catch a tennis ball than cricket ball through moving with the same velocity.

Note:
One should always remember that the impact of an object is due to the impulse per unit area that the object is going to cause. Here since the area of the catcher’s hand is the same for both balls, we can let area go off as a parameter. Hence, we only compare the impulses. But since the time required to catch the ball can be assumed to be the same, we can say that we can just limit our comparison to the forces exerted by the two balls.