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SHM of a particle released in a tunnel through the earth

This type of question, asked 2 times: 2021 Paper 25, 25 Jan 2023. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 25

    10
    Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (R/2)(R/2) from the earth's centre, where ' RR ' 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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  2. Question 2

    25 Jan 2023

    17
    Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g100\text{ }g. The time period of the motion of the particle will be (approximately) (Take g=10 m s−2g = 10\text{ }m{\text{ }s}^{- 2}, radius of earth =6400 km= 6400\text{ }km )

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