The acceleration of a freely falling body does not depend on the mass of the body . Show this by deriving an expression for the same

Explanation

To show that the acceleration of a freely falling body does not depend on its mass, we can derive an expression based on Newton's law of gravitation and Newton's second law of motion. Here’s a step-by-step solution:

### Step 1: Understand the Forces Acting on the Body
When a body is falling freely under the influence of gravity, the only force acting on it is the gravitational force exerted by the planet (e.g., Earth, Mars, etc.).

### Step 2: Write Down Newton's Law of Gravitation
According to Newton's law of gravitation, the gravitational force \( F \) acting on a body of mass \( m \) at a distance \( r \) from the center of a planet of mass \( M \) is given by:
\[
...