Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance R2 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:

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2πRg

12πgR

g2πR

answer is A.

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Detailed Solution

At a displacement ’y’ from’O’⇒ma=−mGMrR3sin⁡θ⇒ma=−GMmR3y⇒a=−GMR3y=−gRy Comparing with a=−ω2y⇒ω=gR⇒T=2πω=2πRg

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