A rectangular vessel when full of water takes $10 $ minutes to be emptied through an orifice in its bottom. ......... $\min$ will it take to be emptied when half filled with water
A$9$
B$7$
C$5$
D$3$
Medium
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B$7$
b (b)Time taken to be emptied for h height, $t = \sqrt {\frac{{2h}}{g}} $
and for $\frac{h}{2}$ height, $t' = \sqrt {\frac{{2h/2}}{g}} = \sqrt {\frac{h}{g}} $$\frac{{t'}}{t} = \frac{1}{{\sqrt 2 }} \Rightarrow t' = \frac{t}{{\sqrt 2 }} = \frac{{10}}{{\sqrt 2 }} = 7\;minute$
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