Q$2.$ A worn multi$-$plate clutch is used to connect two in$-$line shafts and transmit $7\mathrm{.}5$ kW at $750$ rpm $.$ The contact surfaces have inner and outer diameters of $90$ and $140$ mm respectively, and there are $3$ plates. $=0\mathrm{.}3.$ Calculate:

$($a$)$ The axial thrust required. $923$ Nm

$($b$)$ The contact pressures at the inner radius $83\mathrm{.}95kN{m}^2$

$($c$)$ The contact pressures at the outer radius. $130kN{m}^2$