A wall is hit elastically and normally by ' $n$ ' balls per second. All the balls have the same mass ' $m$ '…
A wall is hit elastically and normally by ' $n$ ' balls per second. All the balls have the same mass ' $m$ ' and are moving with the same velocity ' $u$ '. The force exerted by the balls on the wall is
$2 \mathrm{mnu}^2$
$2 \mathrm{mnu}$
$\frac{1}{2} \mathrm{mnu}^2$
$\mathrm{mnu}$
Solution
The correct option is (B).
Force is related to momentum change by following relation,
$\mathrm{F}=\frac{\mathrm{dp}}{\mathrm{dt}}$
Momentum change per second, $\frac{\mathrm{dp}}{\mathrm{dt}}=\mathrm{n}(\mathrm{mu}-(-\mathrm{mu}))=2 \mathrm{nmu}$
Therefore,
$\mathrm{F}=2 \mathrm{nmu}$