$($a$)$ Derive the J$.$ F$.$ Archard's Adhesive Wear Equation stating clearly the assumptions

made.

$($b$)$ An experiment has been carried out on a Pin$-$on$-$Disc machine for sliding contact of

mild steel pin of $8$ mm diameter with EN$31$ disc. The Disc was rotating at $800r.p.m.$ and

the pin was located at a distance of $80$ mm from the centre of the disc. If after $5$ hours of

ruming in dry condition with a normal loud or $5$ kg $,$ al loss of $7\mathrm{.}5$ mg from pin material

has been measured with the help of electronic weighing balance, find out the Archard's

Wear Coefficient and Archard's Wear Equation for mild steel pin. Given that