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JEE Main202126 Feb 2021Morning ShiftPhysicsOscillationsActual

Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance R 2 from the earth's centre, where R is the radius of the earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period:

Options

  1. A1 2 π g R
  2. B2 π R g
  3. Cg 2 π R
  4. DImage is virtual, opposite side of convex mirror.

Correct answer

B. 2 π R g

Step-by-step solution

Force along the tunnel F = - G M m r R 3 cos θ F = - g m R x G M R 2 = g ,   r cos θ = x a = - g R x ω 2 = g R T = 2 π R g

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