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 the free surface and A that of vessel, time t taken to be empited the tank, \[t=\frac{A}{{{A}_{0}}}\sqrt{\frac{2H}{g}}\] \[\therefore \] \[\frac{{{t}_{1}}}{{{t}_{2}}}=\sqrt{\frac{{{H}_{1}}}{{{H}_{2}}}}\] \[\Rightarrow \] \[\frac{t}{{{t}_{2}}}=\sqrt{\frac{{{H}_{2}}}{{{H}_{1}}/2}}\] \[\Rightarrow \] \[\frac{t}{{{t}_{2}}}=\sqrt{2}\] \[\therefore \] \[{{t}_{2}}=\frac{t}{\sqrt{2}}=\frac{10}{\sqrt{2}}=5\sqrt{2}\]\[\approx 7\,\min \]
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