Question

A ball of mass m moving with a velocity v rebounds from a wall. The collision is assumed elastic and the force of interaction between the ball and wall varies as shown in figure. Then, the value of $F_0$ is :

• A. $\frac{mu}{T}$
• B. $\frac{2mu}{T}$
• C. $\frac{4mu}{T}$
• D. $\frac{mu}{2T}$

Answer 1

The correct option is C $\frac{4mu}{T}$

Area under the F-t graph gives the change in momentum of the body during that period.

$\therefore$ $\Delta P=\frac{1}{2}{F}_{o}T$

Also as the collision of ball with the wall is elastic, thus the ball colliding with the wall with initial speed $v$ rebounds with the same speed $u$.

Thus the change in momentum of ball $\Delta P=mu-(-mu)=2mu$

$\therefore$ $\frac{F_{o}T}{2}=2mu$ $⟹F_o=\frac{4mu}{T}$