Question

The terminal velocity $\left(V_c\right)$ of a small sphere falling under gravity in a viscous liquid is related to its radius as

• A. $V_c\propto r$
• B. $V_c\propto \frac{1}{r}$
• C. $V_c\propto r^2$
• D. $V_c\propto r^3$

Answer 1

Answer: (C)

$V_c\propto r^2$

The terminal velocity $V_c$ of the body of radius $r$, density $\rho$ falling through a medium of density ${\rho }_o$ is given by
$V_c=\frac{2r^2(\rho -{\rho }_o)g}{9\eta }$ where $\eta$ is the coefficient of viscosity of medium.
clearly $V_c\propto r^2$