A ball of radius \(r\) and density \(\rho\) falls freely under gravity through a distance \(h\) before entering the water. The velocity of the ball does not change even on entering the water. The viscosity of water is \(\eta\), the value of \(h\) is given by?
1
\(\dfrac { 2 }{ 9 } { r }^{ 2 }\left( \dfrac { 1-\rho }{ \eta } \right) g\)
2
\(\dfrac { 2 }{ 81 } { r }^{ 2 }\left( \dfrac { \rho -1 }{ \eta } \right) g\)
3
\(\dfrac { 2 }{ 81 } { r }^{ 4 }{ \left( \dfrac { \rho -1 }{ \eta } \right) }^{ 2 }g\)
4
\(\dfrac { 2 }{ 9 } { r }^{ 4 }{ \left( \dfrac { \rho -1 }{ \eta } \right) }^{ 2 }g\)