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 $W_{\text{eff }}(=mg$ - buoyant force)
The terminal velocity $v_f$ of the ball is attained when net force on the ball is zero.
$\therefore$ Viscous force $6\pi \eta r{v}_f=W_{\text{eff }}$
When the ball acquires $\frac{2}{3}rd$ 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 $a/3$