Question:
A solid sphere of volume \(V\) experiences a viscous force \(F\) when descending with a speed \(v\) in a liquid. If another solid sphere of volume \(27V\) descends with the same speed \(v\) in the same liquid, it experiences a viscous force
A solid sphere of volume \(V\) experiences a viscous force \(F\) when descending with a speed \(v\) in a liquid. If another solid sphere of volume \(27V\) descends with the same speed \(v\) in the same liquid, it experiences a viscous force
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If sphere volume changes by a factor of \(27\), radius changes by a factor of \(3\).
Updated On: Apr 29, 2026
- \(12F\)
- \(4F\)
- \(9F\)
- \(3F\)
- \(6F\)
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Verified By Collegedunia
The Correct Option is D
Solution and Explanation
By Stokes' law:
\[
F=6\pi \eta rv
\]
So viscous force is proportional to radius:
\[
F\propto r
\]
Now volume of sphere:
\[
V\propto r^3
\]
If volume becomes \(27V\), then radius becomes:
\[
r'=\sqrt[3]{27}\,r=3r
\]
Therefore,
\[
F' = 3F
\]
Hence,
\[
\boxed{(D)\ 3F}
\]
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