A) \[T=2h/v\]
B) \[\text{T=}\sqrt{\left( \frac{\text{2h}}{\text{g}} \right)\text{+}\frac{\text{h}}{\text{v}}}\]
C) \[\text{T=}\sqrt{\left( \frac{\text{2h}}{\text{g}} \right)}\text{+}\frac{\text{h}}{\text{g}}\]
D) \[\text{T=}\sqrt{\left( \frac{\text{h}}{\text{2g}} \right)}\text{+}\frac{\text{2h}}{\text{v}}\]
Correct Answer: B
Solution :
Time taken by the stone to reach the water level \[{{t}_{1}}=\sqrt{\frac{2h}{g}}\] Time taken by sound to come to the mouth of the well, \[{{\text{t}}_{\text{2}}}\text{=}\frac{\text{h}}{\text{v}}\] \[\therefore \]Total time \[{{\text{t}}_{\text{1}}}\text{+}{{\text{t}}_{\text{2}}}\text{=}\sqrt{\frac{\text{2h}}{\text{g}}}\text{+}\frac{\text{h}}{\text{v}}\]
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