A rectangular plate of mass M and dimension `axxb` is held in horizontal position by striking n small balls (each of mass m) per unit area per second. The balls are striking in the shaded half region of the plate. The collision of the balls with the plate is elastic. What is v? `(Given n=100, M =3 kg, m=0.01 kg, b = 2m, a =1m, g = 10m/s^2).`

Answer

`10 ms^(-1)`

Explanation

Since the plate is held horzontal therefore net torque acting on the plate is zero.

`rArr Mg xx (b)/(2) xx F xx (3b)/(4)` ….(i)
`F = n (dp)/(dt) xx ("Area") = n xx (2mv) xx a xx (b)/(2)` ….(ii)
From (i) and (ii) `Mg xx (b)/(2) = n xx (2mv) xx a xx (b)/(2) xx (3b)/(4)`
`rArr 3 xx 10 = 100 xx 2 xx 0.01 xx v xx 1 xx (3 xx 2)/(4)`
`rArr v = 10 m//s`