A planet of radius R = 1 10 × (radius of Earth) has the same mass density as Earth. Scientists dig a…

A planet of radius R=110× (radius of Earth) has the same mass density as Earth. Scientists dig a well of depth R5 on it and lower a wire of the same length and of linear mass density 10-3 kgm-1 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 =6×106 m and the acceleration due to gravity of Earth is 10 ms-2 )
  1. 96 N
  2. 108 N
  3. 120 N
  4. 150 N

Solution

Inside planet
gi=gsrR=43Gπrρ
Force to keep the wire at rest (F)
= weight of wire
=∫4R5Rλdr43Gπrρ=43Gπρ9λ50R2
Here, ρ= density of earth =Me43πRe2
Also, R=Re10 ; putting all values, F=108 N

Asked in: JEE Advanced 2014 (Paper 2)

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