Gravitational Force and Mass Proportionality:

Gravitational force is the attractive force that exists between any two objects with mass. According to Newton's law of universal gravitation, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Mathematically, the gravitational force (F) can be expressed as:

F = G * (m1 * m2) / r^2

Where:
- F is the gravitational force between the two objects
- G is the gravitational constant
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects

The Concept of Weight:

Weight is the force experienced by an object due to the gravitational attraction of a massive body, such as the Earth. It is the product of an object's mass and the acceleration due to gravity.

Weight (W) = mass (m) * acceleration due to gravity (g)

Acceleration Due to Gravity:

The acceleration due to gravity is the same for all objects near the Earth's surface and is denoted by the symbol 'g.' Its value is approximately 9.8 m/s^2. This means that all objects, regardless of their mass, experience the same acceleration when falling freely near the Earth's surface.

Effect of Mass on Gravitational Force:

The gravitational force acting on an object is directly proportional to its mass. This implies that as the mass of an object increases, the gravitational force on it also increases. However, the acceleration experienced by the object due to gravity remains the same.

Equal Acceleration:

When an object is dropped near the Earth's surface, both a heavy and light object will experience the same acceleration due to gravity. This is because the acceleration is determined by the gravitational field strength, which is the same for all objects near the Earth's surface.

Therefore, even though the gravitational force on a heavier object is greater, its greater mass also requires a greater force to accelerate it. As a result, the heavier object and the lighter object fall at the same rate.

Conclusion:

In summary, the gravitational force acting on an object is directly proportional to its mass, but the acceleration due to gravity remains the same for all objects near the Earth's surface. Therefore, a heavy object does not fall faster than a light object because the greater force required to accelerate the heavy object is balanced by its greater mass.