Question

A metal plate of mass $200\text{gm}$ is balanced in mid – air by throwing 40 balls /sec, each of mass $2\text{gm}$, vertically upwards from below. The balls rebound with the same speed with which they strike the plate. Find the velocity with which the balls strike the plate. (Take $g=9.8m/s^2$)

• A. $20\text{m/s}$
• B. $12.25\text{m/s}$
• C. $10\text{m/s}$
• D. $5\text{m/s}$

Answer 1

The correct option is B $12.25\text{m/s}$

Number of balls striking the metal plate per second $=n=40$
Force exerted by the balls per second on the metal plate, taking downward direction as positive
$F=\frac{nm(v-(-u\left)\right)}{t}=\frac{nm(v+u)}{t}=\frac{nm\left(2u\right)}{t}$
($\because$ velocity of the ball remains same)
As the plate is balanced in the mid-air it means weight of the metal plate is balanced by the force exerted the balls.
$\Rightarrow 0.2\times 9.8=\frac{40\times 2\times {10}^{-3}\times 2u}{1}$
$\Rightarrow u=12.25\text{m/s}$