# Pulleys and strings

In the above figure, $$P_{1}$$ and $$P_{2}$$ are massless pulleys, $$P_{1}$$ is fixed and $$P_{2}$$ can move. Masses $$A,B$$ and $$C$$ are $$\dfrac{9m}{64},2m$$ and $$m$$ respectively. All surfaces are smooth and the string is massless. If it is given that $$\theta=\tan^{-1}\left(\dfrac{3}{4}\right)$$, find the magnitude of acceleration of block $$C$$ in $$\text{ms}^{-2}$$.

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