Two geometrically identical homogeneous balls are manufactured of different materials. Their densities ball-`1` and ball-`2` are `800 kg//m^(3)` and `200 kg//m^(3)` respectively. Both balls are dropped from very high tower. Assume that the air resistance is proportional to the square of velocity. Determine the ratio of the maximum velocities of the ball -`1` to ball-`2`.

Options

A. `2`
B. `3`
C. `4`
D. `6`

Explanation

To solve the problem of determining the ratio of the maximum velocities of two geometrically identical homogeneous balls made of different materials, we can follow these steps:

### Step 1: Understand the forces acting on the balls
When a ball is dropped, two main forces act on it:
- The weight of the ball (downward force), given by \( mg \), where \( m \) is the mass of the ball and \( g \) is the acceleration due to gravity.
- The air resistance (upward force), which is proportional to the square of the velocity, represented as \( F_v = c v^2 \), where \( c \) is a constant and \( v \) is the velocity.

### Step 2: Establish the condition for terminal velocity
...