A) \[9\,\,\min \]
B) \[7\,\,\min \]
C) \[5\,\,\min \]
D) \[3\,\,\min \]
Correct Answer: B
Solution :
If \[{{A}_{0}}\] is the area of orifice at the bottom below free surface and \[A\] that of vessel, time \[t\] taken be empited the tank, \[t=\frac{A}{{{A}_{0}}}\sqrt{\frac{2H}{g}}\] \[\therefore \] \[\frac{{{t}_{1}}}{{{t}_{2}}}=\sqrt{\frac{{{H}_{1}}}{{{H}_{2}}}}\] \[\Rightarrow \] \[\frac{t}{{{t}_{2}}}=\sqrt{\frac{{{H}_{2}}}{{{H}_{1}}/2}}\] \[\Rightarrow \] \[\frac{t}{{{t}_{2}}}=\sqrt{2}\] \[\therefore \] \[{{t}_{2}}=\frac{t}{\sqrt{2}}=\frac{10}{\sqrt{2}}=5\sqrt{2}\]
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