• # 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

 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 $=\frac{a}{3}$