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:
Weight of a body of mass m at the Earths surface, W = mg = 250 N
Body of mass m is located at depth, d = (1/2)Re
Where,
Re = Radius of the Earth
Acceleration due to gravity at depth g (d) is given by the relation:
g prime = (1 - (d / Re)g
= [1 - (Re / 2Re) ]g = (1/2)g
Weight of the body at depth d,
W prime = mg prime
= m × (1/2)g = (1/2) mg = (1/2)W
= (1/2) × 250 = 125 N
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