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From a uniform solid spherical planet of radius R,density a, a solid spherical material of radius 2R/3 is scooped out to leave an eccentric hole as shown.Acceleration due to gravity on the surface of the planet before scooping is g and mass of planet left after scooping is M. Aparticle of same mass M is kept at the end of the eccentric hole as shown in the figure and the system id released from rest. Assuming head-on elastic collision between particle and the planet and particle and Newton’s law of gravitation to be valid, after what time will the particle come back to the initial position for the first time?

From a uniform solid spherical planet of radius R,density a, a solid spherical material of radius 2R/3 is scooped out to leave an eccentric hole as shown.Acceleration due to gravity on the surface of the planet before scooping is g and mass of planet left after scooping is M. Aparticle of same mass M is kept at the end of the eccentric hole as shown in the figure and the system id released from rest. Assuming head-on elastic collision between particle and the planet and particle and Newton’s law of gravitation to be valid, after what time will the particle come back to the initial position for the first time?

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