Question

When a ball is released from rest in a very long column of viscous liquid, its downward acceleration is '$a$' (just after release). what must be 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

Answer 1

The correct option is A $\frac{a}{3}$


When the ball is just released, the net force on ball is
$W_{eff}=mg-buoyantforce$


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 $=\frac{a}{3}$