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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

A tunnel is excavated along a chord of the earth at a perpendicular distance R/2 from the centre of the earth. Assuming the tunnel wall to be frictionless, determine the force exerted by the wall on a particle of mass m when it is situated at a distance x from the centre of the tunnel.

Options

  1. AGM_e m R^3 x^2 + R^2 4
  2. BGM_e m x R^3
  3. CGM_e m 2R^2
  4. DGM_e m R^2

Correct answer

C. GM_e m 2R^2

Step-by-step solution

Let the centre of the Earth be the origin (0,0) . The tunnel is excavated at a perpendicular distance R 2 from the centre, so it can be considered along the line y = R 2 . The position vector of the particle at a distance x from the centre of the tunnel is r = x i + R 2 j . The gravitational force on a particle of mass m inside the Earth at position r is directed towards the centre and is given by: F = - GM_e m R^3 r Substituting the position vector of the particle: F = - GM_e m R^3 ( x i + R 2 j ) The force exerte

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