Question

A disc of mass 10 g is kept floating horizontally by throwing 10 marbles per second against it from below. The marbles strike the disc normally and rebound downwards with the same speed. If the mass of each marble is 5 g, the velocity with which the marbles are striking the disc is $(g=9.8m/s^2)$

• A. $0.98m/s$
• B. $9.8m/s$
• C. $1.96m/s$
• D. $19.6m/s$

Answer 1

The correct option is A $0.98m/s$

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=$m\ast 2v=2mv$

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

$=Mg=2mnv$

$v=\frac{Mg}{2mn}=\frac{(0.010\ast 9.8)}{(2\ast 0.005\ast 10)}$

$=0.98m/s$