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Imagine a narrow tunnel between the two ...

Imagine a narrow tunnel between the two diametrically opposite points of the earth. A particle of mass m is released in this tunnel . The time period of oscillation is

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Assume that as narrow tunnel is dug between two diametrically opposite points of the earth. Treat the earth as a solid sphere of uniform density. Show that if a particle is released in this tunnel, it will execute a simple harmonic motion. Calculate the time period of this motion.

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