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

Answer 1

question is to be solved by balancing the torque. Torque is because of gravity and impulse imparted by the balls. impulsive force by the balls can be considered to be acting at the center of the shaded region and mag is acting at the center of the plate.
$Mgb/2=n\left(2mv\right)\left(\frac{3b}{2}\right)\Rightarrow v=\frac{Mgb}{6nm}=\frac{3\times 10\times 2}{6\times 100\times 0.01}=10m/s$