A spherical ball of radius r and density ρₛ is released from rest at height h above the free surface of a liquid of density ρₗ. Air resistance is negligible. Immediately after entering the liquid, the ball continues with constant speed and Stokes' law is valid. What is the coefficient of viscosity η of the liquid?
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Question

A spherical ball of radius r and density ρₛ is released from rest at height h above the free surface of a liquid of density ρₗ. Air resistance is negligible. Immediately after entering the liquid, the ball continues with constant speed and Stokes' law is valid. What is the coefficient of viscosity η of the liquid?

Options

G1 Physics · Accepted Answer

The ball is released from rest through height h. Hence its speed just before entering the liquid is u = √(2gh). The problem states that immediately after entering the liquid it moves with constant speed. Therefore the entry speed is already the terminal speed: vₜ = √(2gh). For Stokes motion, vₜ = 2r²(ρₛ−ρₗ)g/(9η). Thus, √(2gh) = 2r²(ρₛ−ρₗ)g/(9η). Solving for η, η = 2r²(ρₛ−ρₗ)g/ [9√(2gh)]. Correct option: A.