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Question

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 ms2
Speed of sound in air, v=343 ms1


  1. 0.3 s

  2. 20 s 

  3. 20 s

  4. 20+0.3 s


Solution

The correct option is D

20+0.3 s


The question can be divided into two parts, where in the first part, the time taken by the pebble to reach the bottom is calculated and in the second part, the time taken by the sound wave to reach the top is calculated.
Given: 
Initial velocity, u=0 ms1
Depth of the well, s=100 m
Acceleration, a=10 ms2
Speed of sound, v=343 ms1

Let t1 be the time taken by the pebble to hit the bottom.
From second equation of motion,
s=ut1+12at21
100=(0×t1)+(12×(10)×t21)
100=5t21
t1=20 s

We know, time=distancespeed
Let t2 be the time taken for the sound wave to reach from the bottom to the top of the well.
t2=sv=1003430.3 s

Total time,
t=t1+t2
  =20+0.3 s.

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