# Free Fall

## Free Fall

A free-falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall.

Visualizing motion during Free Fall:

When we drop a Rock, let’s say from top floor of a building, then till it reaches the ground the Rock is said to be in a free fall motion. So, what is the definition of free fall?

It is defined as a situation when a body is moving only under the influence of earth’s gravity. Since external force is acting on the ball the motion will be accelerated. This free fall acceleration is also known as acceleration due to gravity.

Let us find the value acceleration due to gravity during free fall. To find this we take one assumption that the height from which the ball is dropped is very small as compared to the radius of the earth.

Force acting during free fall = Force of gravitation between earth and ball

$$F\,\,=\,\,\frac{GMm}{{{(R+h)}^{2}}}$$,

We have assumed,

R + h ∽ R

$$F\,\,=\,\,\frac{GMm}{{{R}^{2}}}$$ … (1)

According to Newton’s second law,

F = ma

Free fall acceleration or acceleration due to gravity is represented by ‘g’.

F = mg … (2)

Using equation (1) and (2),

$$mg\,\,=\,\,\frac{GMm}{{{R}^{2}}}$$,

$$Acceleration\,\,due\,\,to\,\,Gravity(g)\,\,=\,\,\frac{GM}{{{R}^{2}}}$$.