**Gravitational Potential Energy**

In the position of a particle changes on account of conservative force acting on it, then the changes in its potential energy is just the amount of work done on the body by the conservative forces.

If is the gravitational force acting on a test mass of mass m

_{o}at distance r from the centre of earth, then

Work done in lifting the test mass through displacementby the internal agent

Total work done in lifting the test mass from r

_{1}to r

_{2}(> r

_{1})

Total work done by gravitational field

= Change in potential energy

If the gravitational potential energy at infinity U

_{1}= 0 and r

_{1}=and r

_{2}= r, then

**Gravitational Potential**

Gravitational potential due to gravitational force of the earth is defined as the potential energy of a particle of unit mass at that point.

Potential at position

**Relation Between Potential and Field**

We have

In vector form

**Gravitational Potential Due to Hollow Spherical Shell of Mass M, Radius R**

**Outside Point (r > R)****On the surface (r = R)****Inside the shell (r < R)**

**Gravitational Potential Due to Solid Sphere of Mass M, Radius R**

**Outside point (r > R)****On the surface (r = R)****Inside the sphere (r < R)**

**Gravitational Field for Uniform Solid Sphere of Mass M, Radius R**

**Outside point (r > R)****On the surface (r = R)****Inside point (r < R)**

Variation of (l) with distance (r) from centre

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