# Pulleys and strings

**Classical Mechanics**Level 5

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 \(\text{ms}^{-2}\).