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