Question

A stone is dropped into a well in which the level of water is $h$ below the top of well. If $V$ is the velocity of sound, the time $T$ after which the splash is heard is given by

• A. $T=\frac{2h}{V}$
• B. $T=\sqrt{\frac{2h}{g}}+\frac{h}{V}$
• C. $T=\sqrt{\frac{2h}{g}}-\frac{h}{V}$
• D. $T=\sqrt{\frac{h}{2g}}+\frac{2h}{V}$

Answer 1

The correct option is B $T=\sqrt{\frac{2h}{g}}+\frac{h}{V}$

Timetaken by stone to reach at water level is given as $t_1=\sqrt{\frac{2h}{g}}$
And, time taken by sound to travel distance $h$ is $t_2=\frac{h}{V}$
So, total time to hear the splash is equal to the sum of time taken to reach the stone to water level and time taken by the sound to cover a distance $h$ in upward direction.
$\Rightarrow T=t_1+t_2$
$\Rightarrow T=\sqrt{\frac{2h}{g}}+\frac{h}{V}$