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

gravitational potential energy

The small work done in moving this mass through a small distance PQ = dx is

gravitational-field-intensity1

Thus the total work done in moving the mass ‘m’ from infinity to a point A, distance r from the centre of earth is

hollow sphere

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Thus, the potential energy of mass m at a distance r from the centre of the sphere of mass M is given by

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where physics tutorhence 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:

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Potential:

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gravitational potential energy (inside)

Solid sphere

Gravitational field intensity:

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gravitational potential energy

Potential :

hollow sphere
gravitational potential energy
gravitational field intensity
hollow sphere (At centre r = 0)

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