Four masses, A$,$ B$,$ C$,$ and D$,$ of $1\mathrm{.}5kg,1\mathrm{.}2kg,1\mathrm{.}6kg,$ and $2$ kg $,$ respectively, are

mounted in the same plane on a shaft. The distances of the masses' centers of

gravity from the shaft's axis are $400mm,350mm,500mm,$ and $300$ mm $,$ respectively.

The angular positions of B$,$ C$,$ and D$,$ are respectively, $60,135,$ and $220,$

clockwise from A$.$ Find:

a$)$ the resultant out$-$of$-$balance force on the axis of the shaft, when it is rotating at

$210re\frac{v}{m}in.$

$(18$ marks$)$

b$)$ the magnitude and position of a balance to rotate at an effective radius of

$450$mm$.$