1.

Explain the relation between the gravitational potential energy and the gravitational potential.

Answer»

1. In terms of potential, we can write the potential energy of the Earth-mass system as, Gravitational potential energy (U) = Gravitational potential (Vr) × mass (m)

2. Thus, gravitational potential is gravitational potential energy per unit mass.

∴ Vr = \(\frac{U}{m}\)

3. For any conservative force field, the concept of potential can be defined on similar lines.

4. Gravitational potential difference between any two points in gravitational field can be written as,

V2 – V1 = \(\frac{U_2-U_1}{m}\)

= \(\frac{dW}{m}\)

This is the work done (or change in potential energy) per unit mass.

5. Therefore, in general, for a system of any two masses m1 and m2, separated by distance r, we can write,

U = \(-\frac{Gm_1\,m_2}{r}\)

= (V1)m2

= (V2)m1

Here V1 and V2 are gravitational potentials at r due to m1 and m2 respectively.


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