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There is a rectangular plate of mass $M \mathrm{~kg}$ 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 $n=100, M=3 \mathrm{~kg}, m=0.01 \mathrm{~kg}$; $b=2 \mathrm{~m} ; a=1 \mathrm{~m} ; g=10 \mathrm{~m} / \mathrm{s}^2$.
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Verified Answer
The correct answer is:
10
$F=\frac{\Delta p}{\Delta t}=n \times\left(a \times \frac{b}{2}\right) \times(2 m v)$
Equating the torque about hinge side, we have
$$
n \times\left(a \times \frac{b}{2}\right) \times(2 m v) \times \frac{3 b}{4}=M g \times \frac{b}{2}
$$
Substituting the given values we get,
$$
v=10 \mathrm{~m} / \mathrm{s}
$$
Equating the torque about hinge side, we have
$$
n \times\left(a \times \frac{b}{2}\right) \times(2 m v) \times \frac{3 b}{4}=M g \times \frac{b}{2}
$$
Substituting the given values we get,
$$
v=10 \mathrm{~m} / \mathrm{s}
$$
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