A planet of radius R = (1/10) (radius of Earth) has the same mass density as earth. Scientists dig a well of depth R/5 on it and lower a wire of the same length and of linear mass density 10−3kg/m into it. If the wire is not touching anywhere, the force applied at the top of the wire by a person holding it in place is:(Take the radius of Earth =6×106m and the acceleration due to gravity of Earth is  10m/s2 )

As R=RE10---(1)  ρ=M4π/3R3=ME4π/3RE3=density ⇒M=ME103  g=GMR2 g=G(ME/103)(RE/10)2 g=GME10RE2 ⇒g=gE10---(2)  gdepth=g1−dR gdepth=gR−dR gdepth=gxR---(3) mass per unit length=λ=dmdx ⇒dm=λdx---(4)(where x is the distance from the centre of the planet) force F=mg force of attraction element of wire, dF=(dm)gdepth substitute, F=∫4R/5RλdxgxR F=λgR∫4R/5Rxdx F=9λgR50 substitute equation (1),(2)  F=9λ50gE10RE10=9λgERE5000 F=910−3kg/m310m/s26×106m5000 F=108N