There are forces perpendicular to the rods at the points of contact with the disk but the vectors should be pointed toward the rods, not away from them. Of course, since this is in equilibrium, there is an equal force acting on the disk pointing the way you have it but since the question asked is about the tension in the string, it is the force on the rods you want to find. The vertical component of force on each is W/2. You have three vectors marked "W". Why are there three? The tension forces in the rods are in the direction of the rods and the forces at each end of the extensible string are in the horizontal direction of the string.
i dont see why you think the "forces perpendicular to the rods at the points of contact with the disk but the vectors should be pointed toward the rods, not away from them". in all the worked examples in my book the normal reaction always reacts away from the point of contact towards the object (the disc). how are you supposed to know what direction the normal reactions go in. Is there a rule?
there is no tension in the rods. there is tension in the string. both of the rods are of weight w so w acts downwards for both rods. the disc is also of weight w so this also acts downwards.
in the question its says the rods are freely hinged at o. will there be any forces at this.? usually when something is hinged in a question I was told to split it up into x and y components.
i understand a bit more now. so you get equations by looking at 3 parts of the question . forces on rod ab,forces on rod cd and forces for the whole system. for the whole system i let forces up=forces down and forces right=left. i am now looking at forces on the rods individually. i am still stuck though
here is updated diagram
From sum of forces in the vertical direction you can figure the reaction forces S1 and S2. Then from sum of torques about the hinge point O = zero for either rod you can determine the tension in the string. Try it, and post back with your attempt.