First slide

Rectilinear Motion

Question

The splash is heard 2.05S after the stone is dropped into a well of depth 19.6m The velocity of sound is $(g = 9.8 m / s^{2})$

Moderate

A

372 m/s
B

392 m/s
C

342 m/s
D

352 m/s

Solution

Given that depth of well h=19.6m
Total time taken for both sound and stone is given that t=2.05S
Time taken by the stone to reach the water of well $t_{1} = \sqrt{\frac{2 h}{g}} = \sqrt{\frac{2 \times 19.8}{9.8}}$
$\begin{matrix} = \sqrt{2 \times 2} \\ = 2 S \end{matrix}$
$∴$ Time taken by sound $t_{2} = t - t_{1}$
$= 2.05 - 2 = 0.05 S$
$∴$ Velocity of sound $= \frac{h}{t_{2}}$
$= \frac{19.6}{0.05} = 392 m / s$

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