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 shoen instant, The magnitude of viscous force acting on sphere is

Options

A. `6pieta r v_(0)`
B. `12 pi eta r v_(0)`
C. `18 pi eta r v_(0)`
D. `24 pi eta r v_(0)`

Explanation

Relative to liquid, the velocity of sphere is `2 v_(0)` upwards.
`:.` viscous force on sphere `=6 pietar 2v_(0)` downwards
`=12 pi etarv_(0)` downwards