When a solid moves therough a liquid, the liquid opposes the miotioon with a force F. The magnitude of F depends on the coefficient of viscosity `eta` of the liquid, the radius r of the sphere aknd the speed v of the sphere. Assuming that F is proportional to different powers of these quantities, guess a formula for F using the method of dimension.

Explanation

To solve the problem of determining the formula for the force \( F \) opposing the motion of a solid sphere through a liquid, we will use dimensional analysis. Here’s a step-by-step breakdown of the solution:

### Step 1: Identify the Variables
We know that the force \( F \) depends on:
- The coefficient of viscosity \( \eta \)
- The radius of the sphere \( r \)
- The speed of the sphere \( v \)

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