Problem $1.[10$ Marks$]$

$($a$)$ The following data apply to the C$-$clamp of figure. ISO Metric Threads. Pitch $=1\mathrm{.}75mm($single$-$threaded$).$ Outside diameter $=12mm.$ Root diameter $=9\mathrm{.}853mm.$ Root area $=76\mathrm{.}25m{m}^2.$ Coefficient of thread friction $f=0\mathrm{.}12.$ Coefficient of collar friction $f_c=0\mathrm{.}25.$ Mean collar radius $=6mm.$ Load $W=4000N.$ Operator can comfortably exert a force of $80$ N at the end of the handle. $($a$)$ What length of handle, L $,$ is needed? $($b$)$ What is the maximum shear stress in the body of the screw and where does this exist? $($c$)$ What is the bearing pressure P on the threads? $[5$ Marks$].$

$($b$)$ Find the diameter of four equal size bolts as shown in figure. Take ${}_y=40$MPa. $[5$ Marks$].$

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$].$