$18.$ single$-$cylinder reciprocating engine has a eciprocating mass of $60$ kg $.$ The crank rotates at $60$ rpm and the stroke is $320$ mm $.$ The mass of the revolving parts at $160$ mm radius is $40$ kg $.$ If twothirds of the reciprocating parts and the whole of the reciprocating parts and the whole of the revolving parts are to be balanced, determine the

$($i$)$ balance mass required at a radius of $350$ mm

$($ii$)$ unbalanced force when the crank has turned $\backslash (50^\{\backslash$circ$\}\backslash )$ from the top$-$dead centre

$(36\mathrm{.}57$ kg; $209\mathrm{.}9$ N$)$