A $25-$ tooth pinion running at ${}_{in}=1500rpm$ and transferring

$15\mathrm{.}708$ kW to gear with a Gear Ratio, $g_r,4$:$1$ reduction.

The circular pitch, $p_c,$ is $7\mathrm{.}86$ mm $.$ Determine:

$($a$)$ the number of the teeth on the gear,

$($b$)$ the diameter of both gears

$($c$)$ the tangential force on the pinion, and

$($d$)$ the tangential force on the gear.