Question

A large tank filled with water to a height 'h' is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to h/2 and from h/2 to zero is

• A. $\sqrt{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\sqrt{2}-1$
• D. $\frac{1}{\sqrt{2}-1}$

Answer 1

The correct option is C $\sqrt{2}-1$

Time taken for the level to fall from H to H' $t=\frac{A}{A_0}\sqrt{\frac{2}{g}}[\sqrt{H}-\sqrt{H^{\prime }}]$

According to problem - the time taken for the level to fall from h to $\frac{h}{2}$ $t_1=\frac{A}{A_0}\sqrt{\frac{2}{g}}[\sqrt{h}-\sqrt{\frac{h}{2}}]$

and similarly time taken for the level to fall from $\frac{h}{2}$ to zero $t_2=\frac{A}{A_0}\sqrt{\frac{2}{g}}[\sqrt{\frac{h}{2}}-0]\therefore \frac{t_1}{t_2}=\frac{1-\frac{1}{\sqrt{2}}}{\frac{1}{\sqrt{2}}-0}=\sqrt{2}-1$