$2.$ A single clutch disk $($both sides effective$)$ has an outside diameter $1\mathrm{.}67$ times the inside diameter and is used in an application where $40$ hp is produced at $500$ rpm $.$ The dry operation clutch material has a friction coefficient of $0\mathrm{.}25$ and a maximum facing pressure of $20$ psi $.$ Based on uniform pressure assumption determine the following $($torque reserve is unity$)$;

$($a$)$ Inside and outside clutch diameters.

$($b$)$ Maximum clamping force.

$3.$ Repeat problem $2$ using the uniform wear assumption.