Fluid Mechanics

JEE Main level, single correct, medium

173 of 192

Question 173 of 192

A small spherical ball of radius rr, falling through a viscous medium of negligible density has terminal velocity vv. Another ball of the same mass but of radius 2r2r, falling through the same viscous medium will have terminal velocity:

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Answer: (A) v2\dfrac{v}{2}

Ignoring buoyancy force, we can write terminal velocity as
mg=6πηrvmg=6\pi \eta rv
⇒v∝1r\Rightarrow v\propto \dfrac{1}{r} (as mass is constant)
Now, vv′=r′r\dfrac{v}{v'}=\dfrac{r'}{r}
Asr′=2r\text{As}r'=2r
So v′=v2v'=\dfrac{v}{2}

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