Question

A stone is dropped into a well of depth ${}^{\prime }h"$ . The splash is heard after time $"t"$ . If $"C"$ be the velocity of sound, then -

• A. $t=\sqrt{\frac{gc}{2h}}$
• B. $t=c+gh$
• C. $t=c-v$
• D. $t=\frac{h}{c}+\sqrt{\frac{2h}{g}}$

Answer 1

The correct option is D $t=\frac{h}{c}+\sqrt{\frac{2h}{g}}$

The time taken by stone to cover a distance $h$ is,

$h=\frac{1}{2}g{t_1}^2$

$t_1=\sqrt{\frac{2h}{g}}$

Now, the time taken by sound to cover the distance $h$ is,

$t_2=\frac{h}{c}$

Total time after which the splash is heard is,

$t=t_1+t_2$

$t=\frac{h}{c}+\sqrt{\frac{2h}{g}}$