question_answer

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

A) \[\frac{a}{3}\]

B) \[\frac{2a}{3}\]

C) \[\frac{a}{6}\]

D) none of these

Correct Answer: A

Solution :

When the ball is just released, the net force on ball is \[{{W}_{eff}}\,(\text{= mg}-\text{buoyant}\,\,\text{force})\]

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 \[\frac{2}{3}rd\] of its maximum velocity \[{{v}_{f}}\]

the viscous force is \[=\frac{2}{3}{{W}_{eff}}.\]

Hence net force is \[{{W}_{eff}}-\frac{2}{3}{{W}_{eff}}=\frac{1}{3}{{W}_{eff}}\]

\[\therefore \]      required acceleration is \[=\frac{a}{3}\]