Question

In an experiment to verify Stokes law, a small spherical ball of radius $r$ and density $\rho$ falls under gravity through a distance $h$ in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of $h$ is proportional to (ignore viscosity of air)

• A. $r$
• B. $r ^{4}$
• C. $r^{3}$
• D. $r^{2}$

Answer 1

Answer: (B)

After falling through $h ,$ the velocity be equal to terminal velocity
$\sqrt{2 gh }=\frac{2}{9} \frac{ r ^{2} g }{\eta}\left(\rho_{\ell}-\rho\right)$
$\Rightarrow h =\frac{2}{81} \frac{ r ^{4} g \left(\rho_{\ell}-\rho\right)^{2}}{\eta^{2}}$
$\Rightarrow h \propto r ^{4}$