Pulley on the way down

A rope is wound round a pulley of mass \(M\) and its free end is attached to a mass \(M\) which is pulled down by gravity. At time \(t=0\), the block is set free and begins to drop.

Find the acceleration of the block, \(a\).

Details and Assumptions:

  • The rope does not slip and is massless.
  • If your answer is in the form of \(\dfrac{Ag}{B}\), where \(A\) and \(B\) are coprime positive integers, find \(A+B\).
  • \(g = \SI[per-mode=symbol]{10}{\meter\per\second\squared}\).

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