In the pulley system shown in Fig. $2\mathrm{.}1,$ loads of $10$ kg and $15$ kg are carried on the pulleys B

and D ; the $15$ kg weight will descend when released. Find the tension T and the acceleration

of the $15$ kg weight. $[10$ Marks$]$

A $26$ kg splined shaft, rotating freely at $400$ rpm $,$ and having a radius of gyration of $42\mathrm{.}4$

mm $,$ engages a $14\mathrm{.}6$ kg stationary gear. When engaged, the combined radius of gyration of

shaft and gear is $47\mathrm{.}6$ mm $.$ Find the final rotational speed of the combined shaft and gear. $[5$

Marks$]$