Question

Uniform speed of $2cm$ diameter ball is $20cm/s$ in a viscous liquid. Then, the speed of $1cm$ diameter ball in the same liquid is:

• A. $5cm{s}^{-1}$
• B. $10cm{s}^{-1}$
• C. $40cm{s}^{-1}$
• D. $80cm{s}^{-1}$

Answer 1

The correct option is A $5cm{s}^{-1}$

The terminal velocity $V$ of the body of radius $r$, density $\rho$ falling through a medium of density ${\rho }_o$ is given by

$V=\frac{2r^2(\rho -{\rho }_o)g}{9\eta }$ where $\eta$ is the coefficient of viscosity of medium.

clearly $V\propto r^2$, So we have

$\frac{V_2}{V_1}={\left(\frac{r_2}{r_1}\right)}^2$

$V_2={\left(\frac{1}{2}\right)}^2{V}_1=\frac{20}{4}m/s=5m/s$