Using dimensions show that the viscous force acting on a glass sphere falling through a highly viscous liquid of coefficient of viscosity `eta` is `Fprop eta` av where a is the radius of the sphere and v its terminal velocity.

Explanation

To show that the viscous force \( F \) acting on a glass sphere falling through a highly viscous liquid is proportional to the coefficient of viscosity \( \eta \), the radius of the sphere \( a \), and its terminal velocity \( v \), we can use dimensional analysis. Let's break down the solution step by step.

### Step 1: Establish the relationship
We start by assuming that the viscous force \( F \) is proportional to the coefficient of viscosity \( \eta \), the radius of the sphere \( a \), and the terminal velocity \( v \). This can be expressed as:
\[ F \propto \eta^A a^B v^C \]
where \( A \), \( B \), and \( C \) are the powers to which each variable is raised.
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