A tunnel is dug along a diameter of the earth. Find the force on a particle of mass M placed in the tunnel at a distance x from the center.

Mass of earthM=Vρ=(4/3)πR3ρMass of imaginary sphere of radius x is M' ⇒ M=(4/3)πx3ρ  (or) M∝R3⇒M'M=R'3R3⇒M'M=x3R3⇒M'=Mx3R3---(1) g'=GM'x2=GMx3R3x2 from (1) g'=GMxR3---(2) ⇒F=mg'=mGMxR3from equation(2)