If a person drops a pebble in a well of $100 m$ depth, after how much time will he be able to hear the sound, starting from the time he drops the pebble? (Take $g = 10 m / s^{2}$ and speed of sound $= 343 m / s$ )

$\sqrt{20}$ +0.3sec

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$\sqrt{20}$ sec

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0.3 sec

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None of these

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Solution

The correct option is A
$\sqrt{20}$ +0.3sec

To calculate the total time after which the sound of the pebble hitting the surface of the well reaches the person, we need to calculate two-time intervals:
i. Time taken by the pebble to reach bottom.
ii. Time taken by the sound wave to reach the top.
Time taken by pebble to hit the bottom is calculated as follows:
$s = u t + \frac{1}{2} a t^{2}$
$100 = 5 t^{2}$
$t = \sqrt{20} s$ (for pebble to reach the water)
Now, time for sound to reach the top = $\frac{d i s t a n c e}{s p e e d} = \frac{100}{343} = 0.3 (approx)$ .
Therefore, total $t i m e = (\sqrt{20} + 0.3) s$ .

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Similar questions

If a person drops a pebble in a well of $100 m$ depth, after how much time (in seconds) will he be able to hear the sound?
Given:
Acceleration due to gravity, $g = 10 m s^{- 2}$
Speed of sound in air, $v = 343 m s^{- 1}$

Q. A pebble is dropped freely in a well from its top. It takes

20 s

for the pebble to reach the water surface in the well. Taking

g = 10 m s^{- 2}

and speed of sound

= 330 m s^{- 1}

, find: (i) the depth of water surface from the top, and (ii) the time when echo is heard after the pebble is dropped?

Tinku dropped a stone into a very deep well. He hears the sound 6.53 s after he dropped the stone. Find the depth of the well. Take acceleration due to gravity, $g = 10 \frac{m}{s^{2}}$ and $v_{s o u n d} = 340 \frac{m}{s}$ .

Tinku dropped a stone into a very deep well.He hears the sound 6.53s after he dropped the stone. Find the depth of the well. Take acceleration due to gravity,g=10m/s² and v sound = 340m/s.

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If a person drops a pebble in a well of 100 m depth, after how much time will he be able to hear the sound, starting from the time he drops the pebble? (Take g=10 m/s2 and speed of sound =343 m/s)

If a person drops a pebble in a well of $100 m$ depth, after how much time will he be able to hear the sound, starting from the time he drops the pebble? (Take $g = 10 m / s^{2}$ and speed of sound $= 343 m / s$ )