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