Question

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface ?

Answer 1

Given: The weight of a body on the Earth’s surface is 250 N and the body is situated at a depth of half the radius of Earth.

Acceleration due to gravity at depth is given as,

g ′ =( 1− d R )g

Where, d is the depth below the earth surface, R is the radius of earth and g is the acceleration due to gravity.

By substituting the given values in the above formula, we get

g ′ =( 1− R 2 R )g =( 1− R 2×R )g = 1 2 g

Weight of the body at depth is given as,

W ′ =m g ′

By substituting the given values in the above formula,

W ′ =m× 1 2 g = 1 2 mg = 250 N 2 =125 N

Thus, the weight of the body at depth equal to half the radius of the earth is 125 N.