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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