$($a$)$ A $3-$to$-$l speed reduction drive between two parallel shafts at $0\mathrm{.}8$ m centre distance is being provided by a v $-$belt of mass $0\mathrm{.}5k\frac{g}{m}($see fig Q$3$A below$).$ The diameter of the driving pulley is $200$ mm and the driving shaft rotates at $750re\frac{v}{m}in.$ The driven pulley is $600$ mm diameter. The angle between the sides of the belt $2=40.$ If the maximum belt tension is $500$ N and the coefficient of friction between belt and pulleys is $0\mathrm{.}35,$ determine

$($i$)$ The linear belt speed and the centripetal tension due to that belt speed.

$(4$ marks$)$

$($ii$)$ The angle of lap on each pulley

$(4$ marks$)$

$($iii$)$ The maximum power transmitted by the belt

$(8$ marks$)$

$($b$)$ If a flat belt having the same maximym tension and also having a mass of $0\mathrm{.}5k\frac{g}{m}$ were used in an otheryse identical setup, what would be the maximum power transmission at $750$ rpm $?$

$(4$ marks$)$