An air bubble of radius 1 mm is allowed to rise through a long cylindrical column of a viscous liquid of radius 5 cm and travels at a steady rate of 2.1 cm per sec. if the density of the liquid is `1.47(g)/(c c)`. Its viscosity is nearly `(n)/(2)` poise. Then find the value of n. Assume `g=980(cm)/(sec^(2))` and neglect the density of air.

Explanation

To solve the problem, we will use the principles of fluid mechanics, specifically Stokes' law and the concept of buoyancy. Let's break down the solution step by step.

### Step 1: Understand the forces acting on the bubble
In steady state, the buoyant force acting on the air bubble is equal to the viscous drag force (Stokes' force). The buoyant force \( F_b \) can be expressed as:
\[ F_b = \text{Volume of bubble} \times \text{Density of liquid} \times g \]
The volume \( V \) of the bubble (which is spherical) is given by:
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