Question

A disc of mass 40g is kept floating horizontally by throwing 20 marbles per second against it from below. If the mass of each marble is 4.9 g, then the velocity with which the marbles are striking the disc is (assume that, the marbles strike normally and rebound downward with same speed) 

(a) 9.8 ms^-1 

(b) 4.9 ms^-1 

(c) 5 ms^-1 

(d) 2 ms^-1

Answer 1

Answer is (d) 2 ms^-1

Let velocity of each marble = v 

Change in momentum per second 

= 20[mv-(-mv)] = 40 mv

Force exerted by marble on the disc = 40 mv 

To keep the disc, floating, the force must balances the weight of disc, i.e. 40 mv = Mg

40 x 4.9 x 10^-3 x v = 40 x 10^-3 x 9.8

v = \(\frac{9.8}{4.9}\) = 2 ms^-1