$57.$A motor car engine develops $5\mathrm{.}9$ kW at $2100$ rpm$.$ Find the suitable size of clutch plate having friction lining riveted on both sides to transmit the power, under the following conditions:

$($a$)$ Intensity of pressure on the surface not to exceed $6\mathrm{.}87$ x $104$ Pa$.$

$($b$)$ Slip torque and losses due to wear etc. is $35\%$ of engine torque.

$($c$)$ Coefficient of friction on contact surface is $0\mathrm{.}3.$

$($d$)$ Inside diameter of the friction plate is $0\mathrm{.}55$ times the outside diameter