# Gravitational Potential Energy - L2

Physics

## definition

### Gravitational Potential (V)

The gravitational potential (V) is the gravitational potential energy (U) per unit mass: where m is the mass of the object. Potential energy is equal (in magnitude, but negative) to the work done by the gravitational field moving a body to its given position in space from infinity.

## definition

### Gravitational Potential due to a point mass

Gravitational Potential due to a point mass is given by:

## example

### Field due to different arrangements of shells

Example: Two concentric shells of masses and are having radii and . Find the expression of gravitational field in different regions of shells.

Solution:
A uniform shell has no contribution to the gravitational field inside it from Gauss Law for Gravitation. Using this principle,
gravitational field would be 0 for
gravitational field would be  for
gravitational field would be  for

## definition

### Calculation of Potential Energy

For an object having mass having its center of gravity at height and be the acceleration due to gravity.