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