An electric motor running at 500 rpm drives a low speed pump with a reduction of 1.8: through a pair of spur gears, which have teeth of involute form (module = 6mm). The pinion has 20 teeth. In order that the interference does not take place, find
(i) the maximum working depth,
(ii) the lengths of path of contact arc of contact.
(iii) the maximum velocity of sliding on either side of pitch point.