First slide

Viscosity

Question

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:

Moderate

A

$\frac{a}{3}$
B

$\frac{2 a}{3}$
C

$\frac{a}{6}$
D

none of these

Solution

When the ball is just released, the net force on ball is $W_{eff} (= mg - buoyant force)$
The terminal velocity $' v_{f}'$ of the ball is attained when net force on the ball is zero
$∴$ Viscous force $6 πηr v_{f} = W_{eff}$
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 $W_{eff} - \frac{2}{3} W_{eff} = \frac{1}{2} W_{eff}$
$∴$ Required acceleration = $\frac{a}{3}$

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