The force acting between two bodies is called the gravitational attraction force. When among two bodies ne is earth, then this force is called ‘Gravitational force’ i.e. gravitational force is the force by which the earth attracts the body towards its center. For example, the mango plucked from the tree branch, falls down towards the ground due to this force. Any object dropped from a height falls down due to gravitational force. The velocity of a falling body keeps in increasing with certain acceleration which is called ‘gravitational acceleration.’
“Thus, the acceleration produced by the gravitational force is called gravitational acceleration i.e., rate of increase of velocity of freely falling body with time, is called gravitational acceleration.” It is denoted by g and its value is 9.8 m/s-2. Its value does not depend upon the mass, shape and size of the falling body.
Variation in the value of g is produced due to the following situations:
1. Value of g decreases with the increasing height.
2. Value of g decreases with the increasing depth.
3. Value of g changes with changing place on earth’s surface due to its elliptical shape.
4. Value of g is maximum at poles and minimum at equator due to its rotation about its own axis.
1. Variation of acceleration due to gravity with height: Value of gravitational acceleration on the earth’s surface,
and its value at height h from the earth's surface i.e., at point P.
2. Variation in the value of gravitational acceleration with depth: Gravitational acceleration on the surface of earth,
\(g=\frac{GM_e}{R_e^2}\)
and the value of gravitational acceleration at depth d from earth's surface
\(g'=\frac{GM'_e}{(R_e - d)^2}\)
where, M'e is the mass of earth's part of radius (Re - d).
Therefore, gravitational acceleration decreases with the increasing depth.
\(g'=g(1-\frac{d}{R_e})\).....(1)
i.e., gravitational acceleration will be zero at the center of the earth.
