Question

A disc of mass 10grams is kept floating horizontally by throwing 10 marbles per second against it from below . The marbles strike normally and rebound down with same speed . If mass of each marble is 5 grams the the velocity at which they are striking the disc

Answer 1

Given that:
Mass of disc,M=10g=0.010kg
Mass of each marble,m=5g=0.005kg
Suppose the number of marbles striking the disc per second=n and velocity with which marbles strike disc is v.
Then Weight of disc acting downward=Mg
Change in velocity of marbles when they rebound =v-(-v)=2v
Therefore the change in momentum of each marble when it strikes the disc=m x 2v=2mv
and total momentum imparted per second to the disc=2mnv=The force exerted by the marbles in the upward direction
The disc will remain at rest if the net force acting on it is zero provided it is initially at rest.
Therefore for the disc to remain at rest,
Weight of disc=Upward force on it
or Mg=2mnv
v=Mg/2mn=(0.010 x9.8)/(2x0.005x10)
=0.98 m/s