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 250N on the surface?
Solution
We know acceleration due to gravity at a depth d from the surface of the earth is,
where,
g is acceleration due to gravity at the surface of the earth.
The weight of body of mass m at depth d is,
Wd = mgd = mg
Given,
Weight of the body on the surface = 250 N
Distance of the body, d = R/2
Therefore,
where,
g is acceleration due to gravity at the surface of the earth.
The weight of body of mass m at depth d is,
Wd = mgd = mg
Given,
Weight of the body on the surface = 250 N
Distance of the body, d = R/2
Therefore,
