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. `(a)/(3)`
B. `(2a)/(3)`
C. `(a)/(6)`
D. none of these

Answer

A

Explanation

When the ball is just released the net force on ball is `W_(ef)(=mg-`buoyant force)
The terminal velocity `v_f` of the ball is attained when net force on the ball is zero.
Viscous force `6pietarv_f=W_(ef)`
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)/(2)E_(eff)`
Required acceleration`=(a)/(3)`