3
\includegraphics[max width=\textwidth, alt={}, center]{b486decd-75b8-44bd-889f-2472f1163871-2_570_419_1539_863} A uniform disc, of mass 2 kg and radius 0.2 m , is free to rotate in a vertical plane about a smooth horizontal axis through its centre. One end of a light inextensible string is attached to a point on the rim of the disc and the string is wound round the rim. The other end of the string is attached to a small block of mass 4 kg , which hangs freely (see diagram). The system is released from rest. During the subsequent motion, the block experiences a constant resistance to its motion, of magnitude \(R \mathrm {~N}\). Given that the angular speed of the disc after it has turned through 2 radians is \(5 \mathrm { rad } \mathrm { s } ^ { - 1 }\), find \(R\) and the tension in the string.
[0pt] [9]