A stone is dropped into a well in which the level of water is h below the top of the well. If v is speed of sound in the air, the time T after which the splash is heard is given by
A
T=2hv
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B
T=√2hg+hv
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C
T=√2hg+h2v
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D
T=√h2g+2hv
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Solution
The correct option is BT=√2hg+hv Total time taken to hear the sound of splash = Time taken by stone to reach the water surface inside the well + Time taken by sound of splash to reach the ear through air.
Let t1 be time taken by the stone to reach the water surface h=ut1+12gt21
As stone is dropped, so, u=0 ∴h=12gt21 ⇒t1=√2hg.......(i)
Also, time taken t2 by sound of splash to reach the ear through air is ⇒t2=hv..........(ii) ∴ Total time taken to hear the sound of splash T=t1+t2=√2hg+hv