Question

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

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (B)

When the ball is just released, the net force on ball is $W _{\text {eff }}(=m g$ - buoyant force)
The terminal velocity $v _{ f }$ of the ball is attained when net force on the ball is zero.
$\therefore$ Viscous force $6 \pi \eta r v _{ f }= W _{\text {eff }}$
When the ball acquires $\frac{2}{3} r d$ of its maximum velocity $v_f$ the viscous force is $=\frac{2}{3} W _{\text {eff }}$
Hence net force is $W _{\text {eff }}-\frac{2}{3} W _{\text {eff }}=\frac{1}{3} W _{\text {eff }}$
$\therefore$ required acceleration is $a/3$