Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object? Plss help

This is because the acceleration of objects due to gravity is independent of the mass of the object and is constant for all objects, therefore, all objects fall with the same speed.

Explanation:

The weight of an object or force of gravity acting on an object on the surface of earth is a product of its mass and acceleration due to gravity.

Mathematically, w = mg

where, m=mass of the object; g = acceleration due to gravity

Also, from newton's law of gravitation, gravitational force on the object ,F = GMm/r²

where G is the gravitational constant; M is mass of Earth; m is mass of object; r is the distance of separation between the object and the center of mass of the earth which is approximately the radius of earth.

Since the weight of an object is equal to the force of gravitation acting on it

W = F

mg = GMm/r²

g = GM/r²

The expression above is that of the relationship between the force of gravity acting on a body on the earth's surface, the weight of that body and the acceleration due to gravity, g.

It can be seen that the acceleration due to gravity g is independent of the mass of the object. Therefore, the acceleration of objects due to gravity is constant for all objects and all objects fall with the same speed.

The time of fall of an object is dependent only on the height of fall for a given acceleration due to gravity and it is independent of the object's mass

Explanation:

The gravitational force acting on an object on Earth can be observed as the weight, 'W', of the object which is a function of the mass, 'm', of the object and the relationship between the gravitational force and the mass of the object is given as follows;

W = m × g

Where;

g = The acceleration due to gravitational force = Constant

The relationship between the speed, 'u', and therefore, the time, 't', with which an object falls, the distance or height of fall, 'h', and the acceleration of the motion, 'g' is given as follows;

h = u·t + 1/2·g·t²

Given that the initial velocity of the object, 'u', of the object allowed to fall is u = 0 m/s, we have;

h = u·t + 1/2·g·t² = 0 × t + 1/2·g·t²

h = 0 × t + 1/2·g·t² = 1/2·g·t²

h = 1/2·g·t²

t² = 2·h/g

t = √(2·h/g)

Therefore, the time, 't', it takes every object to fall from a height, 'h', is dependent only on the height, 'h', for a given acceleration due to gravity, 'g' and it is independent of the mass, 'm', of the object.

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