Question

A rectangular vessel when full of water, takes $10min$ to be emptied through an orifice in its bottom. How much time will it take to be emptied when half filled with water?

• A. $9min$
• B. $7min$
• C. $5min$
• D. $3min$

Answer 1

Answer: (B)

$7min$

(b) Time taken to be emptied for $h$ height,

$t=\sqrt{\frac{2h}{g}}$ and for $\frac{h}{2}$ height, $t^{\prime }=\sqrt{\frac{2h/2}{g}}=\sqrt{\frac{h}{g}}$

$\therefore \frac{t^{\prime }}{t}=\frac{1}{\sqrt{2}}\Rightarrow t^{\prime }=\frac{t}{\sqrt{2}}=\frac{10}{\sqrt{2}}=7minute$