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Treat a planet as a uniform density sphere of mass M, radius R, and rotation period T. A large asteroid of mass aM is moving at speed ßR/T. The asteroid collides perfectly inelastically with the planet at its equator while traveling tangentially to the surface of the planet in the same direction as the velocity of the contact point on the equator. What is the rotation period of the planet after the asteroid collides with the planet?

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