Question
A container filled with viscous liquid is moving vertically downwards with constant speed $$3{v_0}.$$ 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 container filled with viscous liquid is moving vertically downwards with constant speed $$3{v_0}.$$ 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 :
$$12\pi \eta r{v_0}$$
Solution :
Relative to liquid, the velocity of sphere is $$2{v_0}$$ upwards.
$$\therefore $$ Viscous force on sphere $$ = 6\pi \eta r2{v_0}\,{\text{downwards}}$$
$$ = 12\pi \eta r{v_0}\,{\text{downwards}}$$
Relative to liquid, the velocity of sphere is $$2{v_0}$$ upwards.
$$\therefore $$ Viscous force on sphere $$ = 6\pi \eta r2{v_0}\,{\text{downwards}}$$
$$ = 12\pi \eta r{v_0}\,{\text{downwards}}$$
