Question

When a solid ball of volume $V$ is dropped into a viscous liquid, then a viscous force $F$ acts on it. If another ball of volume $2V$ of the same material is dropped in the same liquid then the viscous force experienced by it will be

• A. $2nF$
• B. $\frac{nF}{2}$
• C. $2F$
• D. $\frac{F}{2}$

Answer 1

Answer: (C)

$2F$

According to stoke's law Viscous force $F_v=6\pi \eta rv$
& 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.
So $F_v=6\pi \eta r\left(\frac{2r^2(\rho -{\rho }_o)g}{9\eta }\right)=\frac{4\pi (\rho -{\rho }_o)g}{3}\times r^3$
We see that $F_v\propto r^3$
or $F_v\propto V$ (volume)
If the volume doubles, viscous force will also become double. Hence correct option is 'C'.