# Motion of Objects under the Influence of Gravitational Force of the Earth

Let us consider a ball having a mass of 1 kg placed on the surface of the earth. The distance between the ball and the earth is equal to the radius of the earth, since the ball is placed on the surface of the earth. The gravitational force acting between the ball and the earth is now given by,

F = G x Mass of the ball x Mass of the earth / (the distance separating the ball and the earth)2

N

Mass of the earth, Me = 6 x 1024 kg
Radius of the earth, Re = 6.4 x 106 m
Then,

= 9.8 N.

Thus, the gravitational force acting between a ball of mass 1 kg and the earth is 9.8 N.

Each exerts an equal force on the other. But since the mass of the stone is very negligible when compared to that of the earth, the acceleration produced on it is very large and so we see it hurtling down when released from a height. The earth is also attracted by the stone but since its mass is very huge the acceleration produced on it is very negligible.

Question

What will be the force of gravitation acting between a man of mass 60 kg and the earth?

Solution

It can be calculated using the relationship

N.

Where m is the mass of the man, Me is the mass of the earth and R is the radius of the earth. On substituting the values we get,

F =

=

= 586.2 N

This means that the earth is exerting a gravitational force of 586.2 N on the man and the man is also exerting an equal force on the earth.