Question

A stone is dropped into a pond from the top of the tower of height $h$. If $v$ is the speed of sound in air, then the sound of splash will be heard at the top of the tower after a time

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

Answer 1

Answer: (A)

Let $t_1$ be the time taken by the stone to strike the surface of water in the pond.
Using $h = ut + \frac{1}{2} gt^{2}$
$\therefore h = \frac{1}{2}gt^{2}_{1}\quad\left(\because u = 0\right)$
or $t_{1} = \sqrt{\frac{2h}{g}}$
Time taken by sound to reach the top of tower, $t_{2} = \frac{h}{v}$
Total time after which splash of sound is heard
$t = t_{1} + t_{2} = \sqrt{\frac{2h}{g}}+\frac{h}{v}$