Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down - Physics - Gravitation

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?

Ajay Shukla · Accepted Answer

Weight of a body of mass m at the Earth’s surface, W = mg = 250 N Body of mass m is located at depth,

Where,

= Radius of the Earth Acceleration due to gravity at depth g (d) is given by the relation:

Weight of the body at depth d,

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?