Question

A ping-pong ball of mass m is floating in air by a jet of water emerging out of a nozzle. If the water strikes the ping-pong ball with a speed v and just after collision water falls dead, the rate of flow of water in the nozzle is equal to :

• A. $\frac{2mg}{V}$
• B. $\frac{mV}{g}$
• C. $\frac{mg}{V}$
• D. None of these

Answer 1

The correct option is C $\frac{mg}{V}$

Initial speed of the water is $V$ and the final speed of water is zero.

$\therefore$ Force exerted by water on the ball $F_w=\frac{dm}{dt}{V}_{rel}$

$\therefore$ $F_w=\frac{dm}{dt}\times (V-0)=V\frac{dm}{dt}$

As the ball floats in air, thus the weight of ball is balanced by the force by water i.e $F_w=mg$

$\therefore$ $V\frac{dm}{dt}=mg$ $⟹\frac{dm}{dt}=\frac{mg}{V}$