Obtain an expression for the gravitational potential.

Explanation

Gravitational Potential :
The force of attraction on a unit mass situated at a distance x from the centre of earth = `(GM)/(x^(2))`
Work done is displacing the unit mass by a distance dx towards the earth is :
`dW="force" times "displacement"=(GM)/(x^(2))dx`
`therefore` Work done by the force in bringing a unit mass from infinity to the earth.s surface will be :
`" "W=int_(infty)^(R)(GM)/(x^(2))dx=GM(-1/x)_(infty)^(R)`
`" "=GM[(-1)/R+1/infty]=(-GM)/R`
This work done will be the gravitational potential at the surface of earth.
`therefore" "V=(-GM)/R=-gR`.