Question

A ball of mass m moving with a velocity u rebounds from a wall. The collision is assumed to be elastic and the force of interaction between the ball and wall varies as shown in $Fig.$. Then the value of $F_0$ is

• A. $mu/T$
• B. $2mu/T$
• C. $4mu/T$
• D. $mu/2T$

Answer 1

The correct option is C $4mu/T$

We know that area under force-time graph gives change in linear momentum

$area=\frac{1}{2}{F}_{o}T$=change in linear momentum

$v_1=-u,$ negative sign represents initial velocity is in negative x- direction according to our sign convention

$v_2=u,$final velocity is in positive x- direction

initial momentum=$m(-u)=-mu$

final momentum=$mu$

change in linear momentum=$2mu$

$\frac{1}{2}{F}_{o}T=2mu$

$⟹F_o=\frac{4mu}{T}$