Visualizing Motion During A Free Fall

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

What is Free Fall?

Free fall 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.

Free Fall Motion

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),

\(mg\) = \(\frac{GMm}{R^2}\)

\(g\) = \(\frac{GM}{R^2}\) ——– (3)

Where, \(M\) = mass of earth
\(R\) = radius of earth

Now the next that comes to mind is that we have already seen is ‘G’ i.e. Universal Gravitational Constant. Its value remains same everywhere. But is it true for g? From equation (3) we can see that g depends on the dimension of the body i.e. mass and radius. Hence it will not be same everywhere. Also as the acceleration remains constant during free fall motion, so we can use equations of motion. We just have to replace value of acceleration in all the equation with g.

For example, \(v\) = \(u + gt\)

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Practise This Question

In vacuum all freely falling bodies have–