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 h / 2 to zero is

Step-by-step solution

Time taken, t= 2 h g Time taken for the level of water to fall from h to h / 2 to 0 , t₁= 2 g ( h₁ - h₂ )= 2 g ( h - h 2 )= 2 h g (1- 1 2 ) Similarly, time taken for the level of water to fall from h / 2 to 0 . t₂= 2 g ( h 2 -0 ) t₂= 2 h g 1 2 t₁ t₂ = 2 h g (1- 1 2 ) 2 h g 1 2 = ( 2 -1 2 ) 1 / 2 = 2 -1