Question

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 1

Correct Answer - A
KEY CONCEPT Since the plate is held horizontal therefore
net torque acting on the plate in zero.

`rArr Mgxx(b)/(2) = F xx(3b)/(4) ….(i)`
`F =n(dP)/(dt) (Area) = nxx(2mv)xxa xx(b)/(2) ….(ii)`
From (i) and (ii)`
Mgxx(b)/(2) =n xx(2mv)xxaxx(b)/(2)xx(3b)/(4)`
`rArr 3xx10 =100 xx2xx0.01xxvzxx1xx(3xx2)/(4)`
`rArr v = 10m/s.`