Question

A disc of mass 10g is kept floating horizontally by throwing 10mrbles/sec against it from below. If the mass of each marble is 5g, calculate the velocity with which the marbles are striking the disc. (Assuming that the marbles strike the disc normally and rebound with the same speed).
A) $\;9.8m/s$
B) $98m/s$
C) $0.98m/s$
D) $0.098m/s$

Answer 1

Hint
First we will try to visualize what is happening in the question. We will calculate what is the change in momentum of the ball in each second. If we calculated it then equate the downward force exerted by the disc to the change in momentum of the marbles and we will get the answer.

Complete step by step solution
Given, Mass of the disc $ = M = 10g = 0.010kg$
Mass of a marble $ = m = 5g = 0.005kg$
Let $v$ be the velocity with which each marble hits the disc.
Now momentum is $ = mv$
$v$ is the change in velocity
$m$ is the mass of the body
Change in the velocity of the marble per rebound is $v - ( - v) = 2v$
So momentum of each marble is $2mv$
And the total momentum exerted by the marbles to disc every second = $2mv(n)$
Where $n$ is the number of marbles hit the disc per second
Now the downward force exerted by the disc is $ = Mg$
Equating these two quantities we get-
$Mg = 2nmv$
$v = \dfrac{{Mg}}{{2nm}}$
Putting values:
$v = \dfrac{{0.010 \times 9.8}}{{2 \times 10 \times 0.005}}$
$v = 0.98m/s$
Hence option (C) is correct.

Note
We can also do it with impulse concept which is:
The product of the average magnitude of a force acting on a body and the time for which it acts.The change in the momentum of a body as a result of a force acting upon it for a short period of time.