Problem $2.[10$ Marks$]$

$($a$)$ A V$-$belt drive is used to connect a motor to a compressor for transmitting $22$ kW from the motor running at $1440$ rpm $.$ The motor pulley is $300$ mm in diameter whereas the compressor pulley which runs at $480$ rpm is $900$ mm $.$ Take coefficient of friction $=0\mathrm{.}2,$ center distance $=1\mathrm{.}2m,$ cross$-$sectional area of belt $=240$ mm $2,$ density of belt material $=1000k\frac{g}{m}3,$ maximum permissible tension in the belt $=900N$ and groove angle $40.$ Find the power capacity of single belt and total number of belts required.$[5$ Marks$].$

$($b$)$ A circular bar is welded to a steel plate. The bar diameter $d=50mm.$ Determine the size of weld required. $[5$ Marks$].$