Aditya's challenges in Mechanics 8

The arrangement shown above consists of a solid cylinder and a solid sphere, each of mass 1 kg1\text{ kg}, on which a light thread is wound. Find the tension in the thread in the process of motion.

The answer is of the form AB\frac{A}{B} for coprime positive integers AA and BB. Find A+BA+B.

Details and Assumptions:

  • The radii of of the cylinder and sphere are equal and are equal to 1m1m

  • Take acceleration due to gravity as g=10 ms1g=10\text{ ms}^{-1}.

  • The friction in the axle of the upper cylinder is assumed to be absent.

  • There is no slipping anywhere.

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