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JEE Main 2024 (31 Jan, Shift 2) · Terminal Velocity

Terminal Velocity question from JEE Main 2024 (31 Jan, Shift 2)

Q29JEE Main 2024 · 31 JAN · SHIFT 2Medium

Terminal Velocity

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 $2r$ , falling through the same viscous medium will have terminal velocity:

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Answer: (d)

Negligible medium density: $v = \dfrac{2r^2\rho g}{9\eta}$ with $\rho = \dfrac{m}{\frac{4}{3}\pi r^3}$ .
So $v \propto \dfrac{m}{r}$ ; same mass, radius doubled.
$v' = \dfrac{v}{2}$
So the answer is (d) $\frac{v}{2}$ .

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