There is a rectangular plate of mass M kg 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 $n=100, \mathrm{M}=3 \mathrm{~kg}, m=0.01 \mathrm{~kg}$; $b=2 m ; a=1 \mathrm{~m} ; g=10 \mathrm{~m} / \mathrm{s}^2$