Question

A container filled with viscous liquid is moving vertically downwards with constant speed $3v_0$. At the instant shown, a sphere of radius r is moving vertically downwards (in liquid) has speed $v_0$. The coefficient of viscosity is $\eta$. There is no relative motion between the liquid and the container. Then at the shown instant, the magnitude of viscous force acting on sphere is:

• A. $6\pi \eta r{v}_0$
• B. $12\pi \eta r{v}_0$
• C. $18\pi \eta r{v}_0$
• D. $24\pi \eta r{v}_0$

Answer 1

Answer: (B)

$12\pi \eta r{v}_0$

Relative velocity of the ball wrt. the liquid is$3v_0-v_0=2v_0$ upward
Substituting $v=2v_0$
Viscous force on the ball is $F_{viscous}=6\pi \eta rv=6\pi \eta r\left(2v_0\right)=12\pi \eta r{v}_0$