Problem $2$: A synchronous belt drive is to have an input sprocket rotational speed of $800$ rpm and an output sprocket speed of $600$ rpm $.$

$($a$)$ List the sprocket combinations that could be used and list the pitch diameters for each sprocket.

$($b$)$ For each sprocket combination from $($a$)$ and using a $1440-8$MGT belt, compute the center distance and the belt linear velocity.