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Question

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

Solution
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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=Re/2
Acceleration due to gravity at depth g(d) is given by the relation:
g=(1dRe)g

g=(1Re2Re)g
=g/2
Weight of the body at depth d,
W=mg
=mg/2=W/2
=125 N

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