$4\mathrm{.}88$ A thin ring with a mass of $2$ kg and radius $r=140mm$ is held against a frictionless wall by a $125-mm$ string $AB.$ Determine $($a$)$ the distance $d,($b$)$ the tension in the string $(c)$ the reaction at

C$.$

The $18-$ft$-$long lightweight gate of Figure $5$ is a quarter circle and is hinged at $H.$ Determine the horizontal

force, $P,$ required to hold the gate in place. Neglect friction at the hinge and the weight of the gate.

Figure $5$