Question

Two spheres of the same material, but of radii R and 3R are allowed to fall vertically downwards through a liquid of density $\sigma$. The ratio of their terminal velocities is

• A. 1 : 3
• B. 1 : 6
• C. 1 : 9
• D. 1 : 1

Answer 1

The correct option is C 1 : 9

Terminal velocity $v=\frac{2g{r}^2(\rho -\sigma )}{9\eta }$

where $\eta$ and $\rho$ is the viscosity of liquid and density of material of sphere, respectively

$⟹$ $v\propto r^2$

Given : $r_1=R$ $r_2=3R$

Thus ratio of velocities $\frac{v_1}{v_2}=\frac{r_1^2}{r_2^2}=\frac{R^2}{9R^2}=\frac{1}{9}$

$⟹$ $v_1=v_2=1:9$