Question

Consider Earth as a uniform solid sphere. gravitational potential at it's surface is v . gravitational potential at it's centre is​

Answer 1

Answer:

F=-dv/dr

but at the centre force will become zero therefore potential energy become constant from centre to the surface

Answer 2

Answer:

$V=-\frac{3}{2}\frac{GM}{R}$

Explanation:

We are given that

Gravitational potential at  earth surface=V

Let R be the radius of earth=R

Mass of earth=M

We have to find the gravitational potential at the center of earth.

Gravitational potential at any point  inside of earth  at distance R from the center is given  by

$V=-GM(\frac{3R^2-r^2}{2R^3})$

At  center of earth r=0

Substitute the value then we get

$V=-GM(\frac{3R^2}{2R^3})=-\frac{3}{2}\frac{GM}{R}$

Hence, the gravitational potential at the center of earth is given by

$V=-\frac{3}{2}\frac{GM}{R}$