Question

There is a rectangular plate of mass $Mkg$ of dimensions $(a\times b)$. The plate is held in horizontal position by striking n small balls each of mass $m$ per unit area per unit time. These are striking in the shaded half region of the plate. The balls are colliding elastically with velocity $v$. What is $v$?

It is given $n=100,M=3kg,m=0.01kg;b=2m;a=1$ $m;g=10m/s^2$

Answer 1

Answer: 10

Let $n$ be the number of balls striking the shaded part of the plate per unit area per unit time.
Taking $T$ about the hinged end, we get
$n(2mv)\times \left(\frac{ab}{2}\right)\times \frac{3b}{4}=Mg\frac{b}{2}$
Therefore,
$v=\frac{2Mg}{2mmab}$
$=\frac{2}{3}\times \frac{3\times 10}{100\times 0.01\times 2}=10m/s$