Question

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

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

Answer 1

The correct option is C $\sqrt{\frac{2h}{g}}+\frac{h}{v}$

Time taken by the stone to reach the water level is given by
$t_1=\sqrt{\frac{2h}{g}}$
Time taken by sound to come to the mouth of the well is
$t_2=\frac{h}{v}$
Thus, total time to hear the splash is given by
$T=t_1+t_2=\sqrt{\frac{2h}{g}}+\frac{h}{v}$