Grade 11 - Physics - Gravitation - Concept of Gravitation

Acceleration due to gravity

The acceleration with which a body falls towards the earth is known as acceleration due to gravity.
The acceleration due to gravity g near the surface of the earth is .

Case 1 :

Let the body of mass m be at a height h from the surface of the earth.If the radius of the earth is R, then as its distance r from the center of the earth is r=(R+h), the downward force on the body is given by,

Where M is the mass of the earth. If the body happens to be very close to the surface, h=0, and the gravitational force on it is-

The acceleration generated due to this gravitational force is, therefore, given by-

The above relation is true for all planets and other heavenly bodies.

(i) Mass of the earth

It is possible to calculate the mass of the earth using the above relation. As radius of the earth ${}^{}$m and, putting weget,

Acceleration due to gravity
(ii) Mean density of the earth
Suppose the mean density of the earth is ,then as

Acceleration due to gravity
Above the surface
The gravitational force acting on a body of mass m when at a height h from the surface of the earth is ,

hence, the body is subjected to a downward acceleration given by,

As ,therefore Where r=(R+h)

NOTE: The above expression shows that the value of acceleration due to gravity decreases with height. It falls inversely with the square of the distance provided the distances are measured from the center of the earth.

Acceleration due to gravity
When (h is negligible to R)
In that condition the relation can be further simplified by using binomial theorem. Accordingly,