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A planet of radius R has an acceleration...

A planet of radius R has an acceleration due to gravity of g on its surface. A deep smooth tunnel is dug on this planet, radially inward, to reach a point P located at a R distance of from the centre of the planet. Assume that the planet has uniform density. The kinetic energy required to be given to a small body of mass m, projected radially outward from P, so that it gains a maximum altitude equal to the thrice the radius of the planet from its surface, is equal to

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