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)

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Answer & Solution

Correct Answer

(B) \(r^{4}\)

Step-by-step Solution

Detailed explanation

After falling through h, the velocity be equal to terminal velocity

\(\sqrt{2 gh }=\frac{2}{9} \frac{ r ^{2} g }{\eta}\left(\rho_{\ell}-\rho\right)\)

\(\Rightarrow h =\frac{2}{81} \frac{ r ^{4} g \left(\rho_{\ell}-\rho\right)^{2}}{\eta^{2}}\)

\(\Rightarrow h \propto r ^{4}\)

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