Question

The gravitational potential at surface of earth is -v0. The mass of earth is M and its radius is R. Find gravitational potential at centre of earth.
zero
-v0
(-v0 + GM/2R)
(-v0 + GM/2R)

Answer 1

Answer:

The potential at the surface is$v=-v_0-\dfrac{GM}{2R}$

Explanation:

Given:

• The potential at the surface of earth $=-v_0$
• Mass of the earth=M
• Radius of the earth=R

We know that the that the variation of gravitational field inside the the under the surface of the earth at a distance r from the centre of the earth is given

$=\dfrac{GMr}{R^3}$

we know that

Let v be the potential at the centre of the earth

$\int\limits^R_0 { \dfrac{GMr}{R^3}} \, dr=\int\limits^{-v_0}_v {} \, dv \\v=-v_0-\dfrac{GM}{2R}$

Hence the potential at the centre of the earth is calculated.