A block $X$ of mass $0.5 kg$ is held by a long massless string on a frictionless inclined plane of inclination $30°$ to the horizontal. The string is wound on a uniform solid cylindrical drum $Y$ of mass $2 kg$ and of radius $0.2 m$ . The drum is given an initial angular velocity, such that the block starts moving up the plane. At a certain instant of time, the magnitude of angular velocity of $Y$ is $10 rad/s$. Calculate the distance travelled by $X$ from that instant of time until it comes to rest.