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A small ball of mass M and density ρ is dropped in a viscous liquid of density ρ₀. After some time the ball falls with a constant velocity. What is the viscous force on the ball?

Asked in JEE Main 6th April 1st Shift 2023 · Stokes' law

• (1) F=Mg(1+ρ/(ρ₀))
• (2) F=Mg(1-(ρ₀)/ρ)
• (3) F=Mg(1±ρρ₀)
• (4) F=Mg(1+(ρ₀)/ρ)

Step-by-step solution

Why the other options are wrong

• (1) comes from inverts the density ratio and adds it; ρ/(ρ₀) exceeds 1 for a sinking ball, so this makes the drag larger than the weight while the ball is still moving down at a steady speed.
• (3) comes from keeps a product ρρ₀, which is not dimensionless, and hedges the sign; the buoyancy is M/ρρ₀g, a ratio, never a product.
• (4) comes from has the right ratio but the wrong sign: buoyancy is an upward push, so it must be taken away from Mg, not added to it.

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