Question

A body of mass $2$ kg collides with a wall with speed 100 $m{s}^{-1}$ and rebounds with same speed. If time of contact was $\frac{1}{50}$ sec, the force exerted on the wall is

• A. $4$ N
• B. $8$ N
• C. ${10}^{4}N$
• D. $2\times {10}^{4}N$

Answer 1

The correct option is D $2\times {10}^{4}N$

Velocity of body initially $u=100\hat{i}m/s$

After bouncing, the body will move with same speed but in opposite direction.

Velocity of body finally $v=-100\hat{i}m/s$

Mass of body $m=2kg$

Change in momentum of the body $\Delta p=m(v-u)=\left(2\right)(-100-100)\hat{i}=-400\hat{i}kgm/s$

Magnitude of change in momentum $|\Delta p|=400kgm/s$

Time of contact $\Delta t=\frac{1}{50}s$

Force exerted on the wall $F=\frac{\Delta p}{\Delta t}=\frac{400}{\left(1/50\right)}=2\times {10}^{4}N$