When a ball is released from rest in a very long column of viscous. Liquid its downwards acceleration is `a` (just after release). Then its acceleration when it has acquired two third of the maximum velocity:

Options

A. 2
B. 3
C. 4
D. 5

Answer

C

Explanation

When the ball is just released, the net force on ball is
`W_(eff) (= mg-` buoyant force )
The terminal velocity `v _(f)` of the ball is attained when net force on the ball is zero.
`therefore` Viscous force `6 pi eta r v _(f) = W _(eff)`
When the ball acquires `2/3` rd of its maximum velocity
`v _(f)` the viscous force is `=2/3 W_(eff)`
Hence net force is `W _(eff) - 2/3 W _(eff) =1/3 W_(eff)`
`therefore` required acceleration is a/3