Translation Converted To Rotation

Classical Mechanics

In the figure above, a body of mass $m$ is tied at one end of a light string and this string is wrapped around the solid cylinder of mass $M$ and radius $R$ . At the moment $t = 0$ the system starts moving. If the friction is negligible, then what is the angular velocity at time $t?$

\frac{{2mgt}}{{R(M + 2m)}}

\frac{{2mgt}}{{R(M - 2m)}}

\frac{{2Mgt}}{{(M + 2m)}}

\frac{{mgRt}}{{(M + m)}}