There is a rectangular plate of mass \( \mathrm{M} \mathrm{kg} \) of dimensions \( (\mathrm{a} \times \mathrm{b}) \). The plate is held in horizontal position by striking \( \mathrm{n} \) small balls each of mass \( \mathrm{m} \) per unit area per unit time. These are striking in the shaded half region of the plate. The balls are colliding elastically with velocity \( \mathrm{v} \). What is \( \mathrm{v} \) ?
\( \mathrm{P} \) It is given \( \mathrm{n}=100, \mathrm{M}=3 \mathrm{~kg}, \mathrm{~m}=0.01 \mathrm{~kg} ; \mathrm{b}=2 \mathrm{~m} ; \mathrm{a}=1 \mathrm{~m} ; \mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2} \).
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