Question

Two metal spheres of densities in the ratio $3:2$ and diameter in the ratio $1:2$ are released from rest in two vertical liquid columns of coefficients of viscosity in the ratio $4:3$. If the viscous force on them is the same then the ratio of their instantaneous velocities is :

• A. $1:2$
• B. $3:2$
• C. $4:3$
• D. $8:3$

Answer 1

The correct option is B $3:2$

According to Stokes law, when a spherical body of radius $r$ is falling in a homogeneous fluid of viscosity $\eta$, the viscous drag acting on body is given by

$F=6\pi \eta rv$

Since viscous drag on both side are equal then,

$6\pi {\eta }_1{r}_1{v}_1=6\pi {\eta }_2{r}_2{v}_2$

So,

$\frac{v_1}{v_2}=\frac{{\eta }_2}{{\eta }_1}.\frac{r_2}{r_1}$

$=\frac{3}{4}\times \frac{2}{1}=3:2$

The ratio of the instantaneous velocities is $3:2$