Give an example for a force proportional to velocity . Prove that terminal velocity of a solid object moving in a viscous medium is directly proportional to square of its size and inversely proportional to the viscoisity of the medium.

Explanation

To solve the problem, we will first provide an example of a force that is proportional to velocity and then prove that the terminal velocity of a solid object moving in a viscous medium is directly proportional to the square of its size and inversely proportional to the viscosity of the medium.

### Step 1: Example of a Force Proportional to Velocity
An example of a force that is proportional to velocity is the viscous drag force experienced by an object moving through a fluid. According to Stokes' Law, the viscous force \( F \) acting on a spherical object of radius \( r \) moving with velocity \( v \) in a viscous medium is given by:
\[ F = -6 \pi \eta r v \]
where \( \eta \) is the viscosity of the fluid. Here, the force is proportional to the velocity \( v \).
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