Question

A stream of glass balls, moving vertically upwards with a speed u, strike a horizontal plate (of mass M) and rebound, therefrom, with the same speed. The disc can be kept floating horizontally, if the number of glass balls (each of mass m), striking it per second, equals.

(1) (2mU/Mg)

(2) (Mg/2mU)

(3) (Mg/mU)

(4) (mU/Mg)

Answer 1

(2) (Mg/2mU)

Let N be the required number of balls striking the plate per second. The change in momentum of each ball, upon striking the plate is

mU - (-mU) = 2mU

∴ Total change in momentum, per second, when N balls strike the ball in one second, is

(2mU) x N = 2mUN.

This rate of change of momentum equals the force exerted on the plate by the glass balls, striking it from below. It is this force that balances the weight of the horizontally floating plate. 

Hence,

2mUN = Mg

∴ N = (Mg/2mU)