Question

A ball of radius r and density ρ falls freely under gravity through a distance h before entering water. Velocity of ball does not change even on entering water. If viscosity of water is η, the value of h is given by

• A.
• B.
• C.
• D.

Answer 1

Answer: (C)

Answer 2

Velocity of ball when it strikes the water surface $v = \sqrt { 2 g h }$

..........(i)

Terminal velocity of ball inside the water

..........(ii)

Equating (i) and (ii) we get $\sqrt { 2 g h } = \frac { 2 } { 9 } \frac { r ^ { 2 } g } { \eta } ( \rho - 1 )$

⇒ $h = \frac { 2 } { 81 } r ^ { 4 } \left( \frac { \rho - 1 } { \eta } \right) ^ { 2 } g$