Question

There is a rectangular plate of mass M kg Df dimensions (a x b). The plate is held in horizontal position by striking n small balls uniformly 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 kg, m = 0 01kg; b = 2 m; a = lm;g = 10 $m/s^2$ . .

Answer 1

$F=\frac{\Delta p}{\Delta t}=n\times (a\times \frac{b}{2})\times (2mv)$
Equating the torque about hinge side, we have
$n\times (a\times \frac{b}{2})\times (2mv)\times \frac{3b}{4}=Mg\times \frac{b}{2}$
Substituting the given values, we get v = 10 m/s