Question Detail
Question
A small metal sphere with diameter 10 mm is dropped into glycerin. The viscous force on the object is 2.5 N. If the terminal velocity of the object is 6 m/s, calculate the coefficient of viscosity η of the fluid.
Correct Answer
Option C is the correct answer.
Detailed Explanation
At terminal velocity, viscous force F = 6πηrv (Stokes' law). Given F = 2.5 N, v = 6 m/s, diameter = 10 mm = 0.01 m, so radius r = 0.005 m. Then η = F/(6πrv) = 2.5 / (6π × 0.005 × 6) = 2.5 / (6π × 0.03) = 2.5 / (0.18π) = 2.5 / (0.5655) ≈ 4.42 N s m⁻².
Hint
Use Stokes' law for the viscous force on a sphere moving through a fluid: F = 6πηrv.