Question

$n$ bullet strike per second elastically on a wall and rebound. What will be the force exerted on the wall by bullets if mass of each bullet is $m$

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

Answer 1

The correct option is C $2mnv$

If a bullet of mass $m$ strikes the wall normally and elastically with speed $v$, then it rebounds along the normal at the same speed. Therefore the change in the momentum of the bullet is $(-2mv)$. But the total momentum is conserved in the collision. Hence the total change in the momentum must be zero. Therefore the momentum change of the wall is $2mv$. If $n$ such bullets strike per second then the momentum change of the wall per second will be $2nmv$. But according to Newton's second law, the momentum change per second is the force experienced by the wall.

Thus the force exerted on the wall by the bullets is,

$F=2mnv$ normal to the wall.