Question

A metal ball $B_1$ (density $3.2g/cc$) is dropped in water, while another metal ball $B_2$ (density $6.0g/cc$) is dropped in a liquid of density $1.6g/cc$. If both the balls have the same diameter and attain the same terminal velocity, the ratio of viscosity of water to that of the liquid is

• A. $2.0$
• B. $0.5$
• C. $4.0$
• D. Indeterminate due to insufficient data

Answer 1

The correct option is B $0.5$

Terminal Velocity

$v_{terminal}=\frac{2}{9}g\frac{r^2}{\eta }[\sigma -\rho ]$

$v_1=v_2$
$\frac{2}{9}g\frac{r^2}{n_w}[{\sigma }_1-{\rho }_w]=\frac{2}{9}g\frac{r^2}{n_1}({\sigma }_2-{\rho }_1)$
$\Rightarrow \frac{n_w}{n_1}=\frac{{\sigma }_1-{\rho }_w}{{\sigma }_2-{\rho }_1}=\frac{3.2-1}{6-1.6}=\frac{1}{2}$