A flat belt drive operates with two pulleys having diameters $315$ mm and $630$ mm respectively. The belt transmits $15$ kW with smaller pulley running at $900$ rpm $.$ The center distance is $2000$ mm $.$ A leather belt is to be used, of which two types of thickness are available : $4\mathrm{.}5$ mm and $8$ mm and one of them is to be selected. The average coefficient of friction between the belt and pulley is $0\mathrm{.}4.$ The allowable stress in the belt is $2\mathrm{.}45$ MPa $.$ The density of leather is $1g\frac{m}{c}{m}^3.$ Assuming a service factor of $1\mathrm{.}6,$ specify the thickness and the width of the belt. The belt width is to be taken from the standard series: $90,112,125,140,160,180,200,225,250,280$ mm $.$

$9$