Two blocks $X$ and $Y$, of mass 2 kg and 4 kg respectively, are connected by a light inextensible string. The string passes over a smooth pulley at the peak of a rough inclined roof. The roof is inclined at an angle $\beta$ where $\cos \beta =\frac{12}{13}$. Block $X$ is on the roof and $Y$ hangs vertically at a height of 2.5 m above the ground. The coefficient of friction between $X$ and the roof is 0.1. The system is released from rest. Given that $Y$ hits the ground before $X$ reaches the pulley.