A small spherical ball of radius \(r\), falling through a viscous medium of negligible density has terminal velocity ' \(v\) '. Another ball of the same mass but of radius \(2 r\), falling through the same viscous medium will have terminal velocity _______.

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{\mathrm{v}}{2}\)

Detailed explanation

Since density is negligible hence Buoyancy force will be negligible at terminal velocity.

\({Mg}=6 \pi \eta \mathrm{rv}\)

\(\mathrm{V} \propto \frac{1}{\mathrm{r}} \quad\) (as mass is constant)

Now, \(\frac{\mathrm{v}}{\mathrm{v}^{\prime}}=\frac{\mathrm{r}^{\prime}}{\mathrm{r}}\)

\(r^{\prime}=2 \mathrm{r}\)

So, \(v^{\prime}=\frac{v}{2}\)

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