$A$ ball of radius $r$ and density $\rho$ falls freely under gravity through a distance $h$ before entering water. The velocity of the ball does not change even on entering the water. If the viscosity of water is $\eta$ and the density of water is $\sigma$ (assumed to be $1$ unit for calculation),the value of $h$ is given by:

• A
  $\frac{2}{9}{r^2}\left( {\frac{{1 - \rho }}{\eta }} \right)\,g$
• B
  $\frac{2}{{81}}{r^2}\left( {\frac{{\rho - 1}}{\eta }} \right)\,g$
• C
  $\frac{2}{{81}}{r^4}{\left( {\frac{{\rho - 1}}{\eta }} \right)^2}g$
• D
  $\frac{2}{9}{r^4}{\left( {\frac{{\rho - 1}}{\eta }} \right)^2}g$