A small ball of mass m and density ρ is dropped in a viscous liquid of density ρ₀. After sometime, the ball falls with constant velocity. The viscous force on the ball is: (a) mg(1 - (ρ₀)/(ρ)) (b) mg((ρ₀)/(ρ) - 1) (c) mg (1 - ρρ₀) (d) mg(1 + (ρ)/(ρ₀))

Answer: (a). At constant velocity: F = mg - B. B = Vρ₀ g = m/ρρ₀ g F = mg(1 - (ρ₀)/(ρ)) So the answer is (a).

A small ball of mass m and density ρ is dropped in a viscous liquid… | JEE Main 2024 (6 Apr, Shift 1)

Q11JEE Main 2024 · 6 APR · SHIFT 1Medium

Viscosity & Stokes' Law

A small ball of mass $m$ and density $\rho$ is dropped in a viscous liquid of density $\rho_0$ . After sometime, the ball falls with constant velocity. The viscous force on the ball is:

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Answer: (a)

At constant velocity: $F = mg - B$ .
$B = V\rho_0 g = \frac{m}{\rho}\rho_0 g$
$F = mg\left(1 - \frac{\rho_0}{\rho}\right)$
So the answer is (a).

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