Question

A cricket ball of mass 100 grams strikes the hand of the player with a velocity of 20 meters per second and is brought to rest in 0.01 seconds. Calculate the force applied by the hand of the player.
A. 2 N
B. 2000 N
C. 200 N
D. 20 N

Answer 1

Here in the question, we need to determine the force applied by the hand of the player on the ball. For this, we need to follow Newton's equation of motion, i.e., force is the product of the mass and the acceleration of the ball.

Complete step by step answer:
As the ball comes to rest in the hand of the player, the final velocity of the ball is 0 meters per second.

From the question $u = 20{\text{ m/sec}}$, $t = 0.01{\text{ sec}}$and $v = 0{\text{ m/sec}}$

Now, following the equation of motion as: $v = u + at$.
Substitute $u = 20{\text{ m/sec}}$, $t = 0.01{\text{ sec}}$and $v = 0{\text{ m/sec}}$ in the equation $v = u + at$ to determine the acceleration of the ball.

$v = u + at \\\ 0 = 20 + a(0.01) \\\ a(0.01) = - 20 \\\ a = \dfrac{{ - 20}}{{0.01}} \\\ = - 2000{\text{ m/se}}{{\text{c}}^2} \\\$

As there is a decrease in the velocity of the ball, so the acceleration comes in negative, which is known as deceleration.

Now, force is the product of the mass of the ball, and the acceleration of the ball, i.e., $F = ma$ where mass should be in kilograms and acceleration should be in meter per square seconds.

In the question, the mass of the ball is given in grams so, converting the mass of the ball in kilograms as: $m = \dfrac{{100}}{{1000}} = 0.1{\text{ kg}}$
Now, substitute $m = 0.1{\text{ kg}}$ and $a = - 2000{\text{ m/se}}{{\text{c}}^2}$ in the formula $F = ma$ to determine the force exerted by the ball on the hand.

$F = ma \\\ = 0.1 \times ( - 2000) \\\ = - 200{\text{ N}} \\\$

Following the newton’s third law of motion, which states that each action has equals and opposite reaction. So, when the ball exerts the force of -200 N on the hand of the player then, the force exerted by the hand on the player is 200 N

Option C is correct.

Note: Students should be noted here that it is mentioned in the question that the ball has come to rest, and that’s why we have taken the final velocity of the ball as zero. Otherwise, we have to calculate the final velocity of the ball by using other newton’s equations of motion.