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?
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Answer 1

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, d = (1/2)Re

Where,

Re = Radius of the Earth

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

g' = (1 - (d / Re)g

= [1 - (Re / 2Re) ]g = (1/2)g

Weight of the body at depth d,

W' = mg'

= m × (1/2)g = (1/2) mg = (1/2)W

= (1/2) × 250 = 125 N

Answer 2

Explanation:

= [1 - (Re / 2Re) ]g = (1/2)g

Weight of the body at depth d,

W' = mg'

= m × (1/2)g = (1/2) mg

= (1/2)W

= (1/2) × 250 = 125 N