A ball of radius r and density $\mathrm{\rho }$ 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 $\mathrm{\eta }$, the value of h is given by

(a) $\frac{2}{9}{\mathrm{r}}^{2}\left(\frac{1-\mathrm{\rho }}{\mathrm{\eta }}\right)\mathrm{g}$

(b) $\frac{2}{81}{\mathrm{r}}^{2}\left(\frac{\mathrm{\rho }-1}{\mathrm{\eta }}\right)\mathrm{g}$

(c) $\frac{2}{81}{\mathrm{r}}^{4}{\left(\frac{\mathrm{\rho }-1}{\mathrm{\eta }}\right)}^{2}\mathrm{g}$

(d) $\frac{2}{9}{\mathrm{r}}^{4}{\left(\frac{\mathrm{\rho }-1}{\mathrm{\eta }}\right)}^{2}\mathrm{g}$

Explanation is a part of a Paid Course. To view Explanation Please buy the course.

Difficulty Level: