A) \[2\pi \,L\]
B) \[\frac{L}{\sqrt{2\pi }}\]
C) L
D) \[\frac{L}{2\pi }\]
Correct Answer: B
Solution :
Velocity of efflux when the hole is at depth h, \[v=\sqrt{2gh}\] Rate of flow of water from square hole \[{{Q}_{1}}={{a}_{1}}{{v}_{1}}\]= \[{{L}^{2}}\sqrt{2gy}\] Rate of flow of water from circular hole \[{{Q}_{2}}={{a}_{2}}{{v}_{2}}\]= \[\pi {{R}^{2}}\sqrt{2g(4y)}\] According to problem \[{{Q}_{1}}={{Q}_{2}}\] Þ \[{{L}^{2}}\sqrt{2gy}=\pi {{R}^{2}}\sqrt{2g(4y)}\] \[\Rightarrow \]\[R=\frac{L}{\sqrt{2\pi }}\]
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