Question

if v0 is the gravitational potential at the center of the earth of radius r then the potential distance of 2R from the center of the earth is
(a) 2v0/3
(b)vo/3
(c)vo/6
(d)vo/4​

Answer 1

Answer:

At the centre, its value becomes equal to (3/2) times of V

We know that the gravitational potential on the surface is equal to

V= —[ (GM) /R] - - - - - - (i)

As the earth is a solid body, on going down the surface the gravitational potential becomes equal to

Ve=−[GM/2(R^3)][3(R^2)−(r^2)]

put r= 0 to find potential at the centre

it will come out to be

Ve = —3/2 [(GM) /R]

from equation (i), we get

Ve = 3/2 V