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 p

Question

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:

TestHub · Accepted Answer

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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