A helical cast steel gear with $30\backslash$deg helix angle has to transmit $35$ kW at $2000$ r$.$p$.$m$.$ If the gear has $25$ teeth, find the necessary module, pitch diameters and face width for $20\backslash$deg full depth involute teeth. The static stress for cast steel may be taken as $100$ MPa. The face width may be taken as $3$ times the normal pitch. The tooth form factor is given by the expression y$\text{'}=0\mathrm{.}154-0\mathrm{.}912/$TE$,$ where I represents the equivalent mum$-6$ ber of teeth. The velocity factor is given by C$,$ where $6+$ v v is the peripheral speed of the gear in m$/$s$.$