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

Weight of a body of mass $$m$$ at the Earth's surface,$$W=mg=250\ N$$Body of mass $$m$$ is located at depth, $$d=R_e/2$$Acceleration due to gravity at depth $$g(d)$$ is given by the relation: $$g'=(1-\dfrac{d}{R_e})g$$$$g'=(1-\dfrac{R_e}{2R_e})g$$     $$=g/2$$Weight of the body at depth $$d$$, $$W'=mg'$$       $$=mg/2=W/2$$       $$=125\ N$$PhysicsNCERTStandard XI

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