JEE Main 2026 Jan 21 Shift 2, Physics Q22: Hydrodynamic

JEE Main2026Jan 21, Shift 2Physics

The terminal velocity of a metallic ball of radius 6 mm in a viscous fluid is 20 cm/s. The terminal velocity of another ball of same material and having radius 3 mm in the same fluid will be _________ cm/s.

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Solution

For a sphere falling through a viscous fluid, terminal velocity scales as $v_{T} \propto r^{2}$ (since $v_{T} = \frac{2 r ^{2} g ( σ - ρ )}{9 η}$ , with $σ, ρ, η$ fixed).

Ratio: $\frac{v _{T, 2}}{v _{T, 1}} = (\frac{r _{2}}{r _{1}})^{2} = (\frac{3}{6})^{2} = \frac{1}{4}$ .

So $v_{T, 2} = \frac{20}{4} = 5$ cm/s.

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JEE Main 2026 Jan 21 Shift 2, Physics Q22: Hydrodynamic

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