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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 :

$\frac{m u}{T}$
$\frac{2 m u}{T}$
$\frac{4 m u}{T}$
$\frac{m u}{2 T}$

A

\frac{m u}{T}

B

\frac{4 m u}{T}

C

\frac{2 m u}{T}

D

\frac{m u}{2 T}

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Solution

Verified by Toppr

Area under the F-t graph gives the change in momentum of the body during that period.
$∴$ $Δ P = \frac{1}{2} F_{o} T$
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 $Δ P = m u - (- m u) = 2 m u$
$∴$ $\frac{F_{o} T}{2} = 2 m u$ $⟹ F_{o} = \frac{4 m u}{T}$

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