JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Fluid Mechanics

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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:

(A) $\frac{V}{2}$ ✓ Correct
(B) $\frac{V}{4}$
(C)4v
(D)2v

Answer: (A)

Solution

At terminal velocity, viscous drag balances weight:

M g = 6 π η r v

. With density negligible, buoyancy plays no role, and since the mass M is fixed,

v \propto \frac{1}{r}

For

r^{'} = 2 r

v^{'} = v \times \frac{r}{r ^{'}} = \frac{v}{2}

JEE Main · 2024 · 31 Jan 2024 · Shift 2 · Single correct option

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