A solid sphere, of radius R acquires a terminal velocity `v_(1)` when falling (due to gravity) through a viscous fluid having a coefficient of viscosity h. The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, `v_(2)`, when falling through the same fluid, the ratio `(v_(1)//v_(2))` equal `9/x`. Find the value of x.

Explanation

To solve the problem, we need to analyze the relationship between the terminal velocities of the solid sphere and the smaller spheres after it is broken down.

### Step-by-Step Solution:

1. **Understanding Terminal Velocity**:
The terminal velocity \( v \) of a sphere falling through a viscous fluid is given by the formula:
\[
v \propto r^2
...