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