Question

A uniform rod of weight 300N and 2m long is hinged to the floor at one end so that it can rotate in the vertical plane. The other end of the rod is tied to a point on the ceiling vertically above the floor hinge by means of a rope 2.5m long. The vertical height if the ceiling above the floor is 3m. Determine the magnitude and direction of the reaction of the hinge and the magnitude of the tension in the rope. Neglect the weight of the rope.

Answer 1

let x be distance from hinge to point below other end of rod
then height of end of rod above floor
= sqrt(4-x^2)
let y be distance down from ceiling to tip of rod
then
y = sqrt(6.25-x^2)
so
3 = sqrt(4-x^2) + sqrt(6.25-x^2)
sqrt(6.25-x^2 )= 3 - sqrt(4-x^2)
6.25 - x^2 = 9 -6sqrt(4-x^2)+4-x^2
-6.75 = -6 sqt(4-x^2)
(1.125^2 = 4-x^2
x^2 = 2.734
x = 1.65 meters
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well, that was the hard part
I suspect you can work it from there with forces and moments balanced.