Q: A ball of relative density 0.8 falls into water from a height of 2 m. Find the depth to which the ball will sink (neglect viscous forces)

Sol:

Initial velocity of the body by touching the water surface u is given by :

$\displaystyle v = \sqrt{2 g h} $

Retardation of the ball moving in downward direction inside the water due to buoyancy force

$\displaystyle -a = \frac{upthrust – weight}{mass} $

$\displaystyle -a = \frac{V \rho_w g – V \rho_b g}{V \times 0.8} $

$\displaystyle – a = \frac{1 \times g – 0.8 g}{0.8} = \frac{g}{4}$

Distance travelled by the body inside the water before coming to rest is given by

$\displaystyle h’ = \frac{v^2}{2a} = \frac{2 g h}{2g/4} = 4 h $

h’ = 8 m