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