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 times taken for the level of water to fall from h to $\frac { h } { 2 }$ and from $\frac { h } { 2 }$ to zero is

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

Answer 1

Answer: (C)

$\sqrt { 2 } - 1$

Answer 2

Time taken for the level to fall from H to $H ^ { \prime }$

$t = \frac { A } { A _ { 0 } } \sqrt { \frac { 2 } { g } } \left[ \sqrt { H } - \sqrt { H ^ { \prime } } \right]$

According to problem- the time taken for the level to fall from

h to $t _ { 1 } = \frac { A } { A _ { 0 } } \sqrt { \frac { 2 } { g } } \left[ \sqrt { h } - \sqrt { \frac { h } { 2 } } \right]$

and similarly time taken for the level to fall from $\frac { h } { 2 }$ to zero

$t _ { 2 } = \frac { A } { A _ { 0 } } \sqrt { \frac { 2 } { g } } \left[ \sqrt { \frac { h } { 2 } } - 0 \right]$