Problems

In a Porter governor, the upper and lower arms are each $200$ mm long, and are each inclined at $30$ to the vertical when the sleeve is in its lowest position. The points of suspension are each $36$ mm from the axis of the spindle. The mass of each rotating ball is $3$ kg $,$ and that of the central load on the sleeve $20$ kg $.$ If the movement of the sleeve is $36$ mim $,$ find the range of speed of the governor.

$($U$.$ Lond.$)$

$($Answer: $170\mathrm{.}6re\frac{v}{m}in$ to $185\mathrm{.}4re\frac{v}{m}in)$