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, \[\operatorname{v}\,\,=\,\sqrt{2gh}\]. Rate of flow of water from square hole \[{{Q}_{1}}={{a}_{1}}{{\nu }_{1}}={{L}^{2}}\sqrt{2gy}\] Rate of flow of water from circular hole \[{{\operatorname{Q}}_{2}}=\,\,{{a}_{2}}{{\nu }_{2}}=\,\,\pi {{R}^{2}}\,\sqrt{2g(4y)}\] According to problem \[{{Q}_{1}}={{Q}_{2}}\] \[\Rightarrow \,\,\,{{L}^{2}}\,\sqrt{2gy}\,\,=\,\,4{{R}^{2}}\,\sqrt{2g(4y)}\,\,\,\Rightarrow \,\,R=\frac{1}{\sqrt{2\pi }}\]
You need to login to perform this action.
You will be redirected in
3 sec
