$(9.)$ A shaft is supported in two bearings $2\mathrm{.}4m$ apart and projects $0\mathrm{.}6m$ beyond the bearings at each end. The shaft carries three pulleys, one at each end and one at the middle of its length. The end pulleys have masses of $90kg$ and $50kg$ and their centres of mass are at $3\mathrm{.}75mm$ and $5mm$ respectively from the shaft axis. The centre pulley has a mass of $70kg$ and its centre of mass is $6-25mm$ from the shaft axis. If the pulleys are arranged so as to give static balance, determine the dynamic forces produced on the bearings when the shaft rotates at $300re\frac{v}{m}in.$

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

$($Answer: $297-4N)$