Question

Assuming the earth to be a sphere of uniform density the acceleration due to gravity

Answer 1

In a mine 2000 km deep, the gravitational force by the outer shell will cancel out. The only gravitational force would be due to the inner sphere. It would be equal to the gravitational force due to a point mass having mass equal to the mass of the inner sphere placed at the center of the earth.

Therefore, Gravitaional force

F = G*(4*pi/3)*r*r*r*d*m/r*r = G*(4*pi/3)*r*m = m*a

=> a = g*r/R = 6000/8000 X g =3g/4

where, G = Universal gravitational constant

r = distance from the center inside the mine = 6000 km

m = mass of the body experiencing the force

d = density of earth

R = radius of earth = 8000 km

a = acceleration due to gravity inside the mine.