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