A) \[\frac{1}{\sqrt{2\pi }}\]
B) \[2\pi L\]
C) \[\sqrt{\frac{2}{\pi }}.\,L\]
D) \[\frac{L}{2\pi }\]
Correct Answer: C
Solution :
[C]Let and be the velocity of efflux from square \[{{v}_{1}}\]and \[{{v}_{2}}\]circular hole respectively\[{{S}_{1}}\] and \[{{S}_{2}}\] be cross-section areas of square and circular holes. |
\[{{v}_{1}}\sqrt{8gy}\]and \[{{v}_{2}}=\sqrt{2g(y)}\] |
The volume of water coming out of square and circular hole per second is |
\[{{Q}_{1}}={{v}_{1}}{{S}_{1}}=\sqrt{8gy}\,\,{{L}^{2}};\] |
\[{{Q}_{2}}={{v}_{2}}{{S}_{2}}=\sqrt{2gy}\,\,\pi {{R}^{2}}\therefore {{Q}_{2}}={{Q}_{2}}\] |
\[\therefore R=\sqrt{\frac{2}{\pi }}.L\] |
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