When a ball is released from rest in a very long column of viscous liquid, its downward acceleration is '$a=3m/s^2$'  (just after release). Then its acceleration in $m/s^2$  when it has acquired two third of the maximum velocity is _____.

When the ball is just released, the net force on ball is  $W_{eff}=(=mg–buoyantforce)$
The terminal velocity $\text{'}{v}_f\text{'}$  of the ball is attained when net force on the ball is zero.
 $\therefore \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Viscous force\hspace{0.17em}}6\pi \eta r{v}_f=W_{eff}$
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  $W_{eff}-\frac{2}{3}{W}_{eff}=\frac{1}{3}{W}_{eff}$
          required acceleration is = $\frac{a}{3}$