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JEE Advanced2014PhysicsGravitationActual

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 - 3 k g m - 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 × 10 6 m and the acceleration due to gravity of Eart

Options

  1. A96 N
  2. B108 N
  3. C120 N
  4. D150 N

Correct answer

B. 108 N

Step-by-step solution

Inside planet g i = g s r R = 4 3 G π r ρ Force to keep the wire at rest (F) = weight of wire = ∫ 4 R 5 R λ d r 4 3 G π r ρ = 4 3 G π ρ 9 λ 50 R 2 Here, ρ = density of earth = M e 4 3 π R e 2 Also, R = R e 10 ; putting all values, F = 108   N

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