Aditya's challenges in Mechanics 8

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

The answer is of the form \(\frac{A}{B}\) for coprime positive integers \(A\) and \(B\). Find \(A+B\).

Details and Assumptions:

  • The radii of of the cylinder and sphere are equal and are equal to \(1m\)

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

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

  • There is no slipping anywhere.


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