# Physics Assignment Help With Gravitational Potential Energy

## 6.3 Gravitational Potential Energy

The gravitational potential energy of a body at a point is defined as the amount of work done in bringing the body from infinity to that point against the field.

To calculate the gravitational potential energy of a mass m placed on the surface of a sphere. Assume uniform sphere of radius R and mass M. let a the body of mass m is placed at P, at a distance x from the centre of sphere. The force acting on this body, when it is at P is The small work done in moving this mass through a small distance PQ = dx is Thus the total work done in moving the mass ‘m’ from infinity to a point A, distance r from the centre of earth is \ <  Thus, the potential energy of mass m at a distance r from the centre of the sphere of mass M is given by and on the surface of earth it is where hence U = Vm. So potential energy of a mass m = potential at that point × mass (m)

6.3.1 Gravitational field intensity and gravitational potential for solid and hollow sphere

### Gravitational field intensity: (outside)   (on the surface) (inside)

### Potential: (outside)  (on the surface) (inside)

Solid sphere

Gravitational field intensity:     ### Potential :    (At centre r = 0)

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