# 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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