c
(c)Time taken for the level to fall from H to \(H'\) \(t = \frac{A}{{{A_0}}}\sqrt {\frac{2}{g}} \,\,\left[ {\sqrt H - \sqrt {H'} } \right]\)
According to problem- the time taken for the level to fall from h to \(\frac{h}{2}\) \({t_1} = \frac{A}{{{A_0}}}\sqrt {\frac{2}{g}} \;\;\left[ {\sqrt h - \sqrt {\frac{h}{2}} } \right]\)
and similarly time taken for the level to fall from \(\frac{h}{2}\) to zero \({t_2} = \frac{A}{{{A_0}}}\sqrt {\frac{2}{g}} \;\left[ {\sqrt {\frac{h}{2}} - 0} \right]\) \(\therefore \;\frac{{{t_1}}}{{{t_2}}} = \frac{{1 - \frac{1}{{\sqrt 2 }}}}{{\frac{1}{{\sqrt 2 }} - 0}} = \sqrt 2 - 1.\)