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 `(h)/(2)` and from `(h)/(2)` to zero is

Options

A. `sqrt2`
B. `1/sqrt2`
C. `sqrt2-1`
D. `(1)/(sqrt2-1)`

Answer

C

Explanation

Time taken for the level to fall from H to H. -
`t= (A)/(A_0)sqrt(2/g)(sqrt(H)-sqrt(H.))`
`(t_1)/(t_2)=(sqrt(h)-sqrt(h/2))/(sqrt(h/2)-0)=(1-1/sqrt2)/(1/sqrt2)=sqrt2 -1`