Given below are two statements:
Statement I: A small steel ball falling through glycerine at its terminal velocity has zero net force acting on it, yet the viscous force on it continues to do work.
Statement II: The terminal velocity of a ball falling through a viscous liquid is directly proportional to its radius.
In the light of the above statements, choose the correct answer from the options given below:
Answer: (B) Statement I is true but Statement II is false
Concept. At terminal velocity the forces balance, but the ball still moves, so each force does work. Stokes' law gives $v_t = \dfrac{2r^2(\rho - \sigma)g}{9\eta}$.
Step 1. Statement I. Net force is zero (weight $=$ buoyancy $+$ viscous force), so the speed is constant. The viscous force acts opposite to the motion while the ball moves, so it does negative work, turning gravitational energy into heat. True.
Step 2. Statement II. $v_t \propto r^2$, not $r$. False.
Answer. Statement I is true but Statement II is false (Option B).
Solution by Sreeraj P, M.Sc Physics