1. Newton’s Law of Universal Gravitation
2. Dimensional formula of G
3. Gravitational Force
4. Gravitational Field
5. Gravitational Potential
6. Definition
7. Equipotential Surface
8. Relation between Gravitational Intensity and Potential
9. Gravitational Potential due to Spherical Shell of Matter
10. Gravitational Field due to Spherical Shell of Matter
Gravitational Potential
“The gravitational potential at a point in a gravitational field is defined as the work done against
the field in bringing a unit mass from infinity to the point considered”. It is a scalar quantity & is
denoted by ‘V’.
\(V=\frac{W}{m}\),Work done against the field in bringing the mass ‘m’ from infinity to the point in question.
But \(dw=-F.dx\)
$$
\therefore V = \frac{W}{m} = \frac{1}{m}\int^{r}_{\infty}dw = \frac{1}{m}\int^{r}_{\infty}-F.dx
$$
$$
= -\frac{1}{m}\int^{r}_{\infty}\left(-\frac{GMm}{x^2}\right).dx
$$
$$
= GM\int^{r}_{\infty}\frac{dx}{x^2}
$$
$$
= GM \left\{-\frac{1}{x}\bigg]^{r}_{\infty}\right\}
$$
$$
=GM\left(-\frac{1}{r}\right)
$$
$$
\therefore V = -\frac{GM}{r}
$$
Here, ‘V’ is the gravitational potential due to the body having mass ‘M’ at a point which is
located at a distance ‘r’ from it.
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