Question

A player caught a cricket ball of 150g moving at a rate of 20m/s. If the catching process is completed in 0.1s, the force of the blow exerted by the ball on the hand of the player is equal to:
(1) 150N
(2) 3N
(3) 30N
(4) 300N

Answer 1

Hint: Apply Newton’s second law of motion. That is, the force is equal to the rate of momentum. The change in momentum which is also known as the impulse is the product of the mass and the velocity. For this first calculate the change in momentum which is the product of mass and change in velocity. This force can be calculated by taking the ratio of change in momentum to the time taken.
Formula used:
$F=\dfrac{dp}{dt}$
where F is the force
$\dfrac{dp}{dt}$ is the rate of change of momentum.

Complete step-by-step solution
$F=\dfrac{dp}{dt}$
where, p=mv
$\Rightarrow p=150\times {{10}^{-3}}\times 20$
$\therefore p=3kgm/s$
Then,
 $\begin{align}
  & F=\dfrac{3}{0.1} \\
 & \therefore F=30N \\
\end{align}$
Thus, option (3) is correct.
Additional information: According to Newton’s second law of motion force is proportional to the acceleration. Or otherwise, a change in momentum is equal to impulse. Where impulse is the product of force and time. For a rigid body, the total momentum of the body will be the sum of individual moments of particles. Since velocity is a vector quantity, momentum is also a vector quantity. That is, which have both magnitudes as well as direction. The momentum has the same direction as velocity since it directly depends on velocity. Momentum can also be described as a type of speed or force of a moving object. Whereas, inertia is the tendency of an object to move on. Thus all the moving objects will have momentum. The momentum of a body depends upon its mass and velocity. Hence the body which has higher mass or velocity will have a greater value of momentum. Thus the momentum of a particle may be explained as the product of its mass and velocity.

Note: The momentum of a body depends upon its mass and velocity. Hence the body which has higher mass or velocity will have a greater value of momentum. The momentum has the same direction as velocity since it directly depends on velocity. Momentum can also be described as a type of speed or force of a moving object. Thus force is equal to the rate of change of momentum.