An object of mass 1.8kg is attached to the ends of two light elastic strings having the same modulus of elasticity. One of the strings has natural length 0.8m and the other has a natural length of 1.1m. The longer string is attached at A and the shorter string is attached at B on the same horizontal level. The object hangs 0.85m below O, a point on the same level as A and B, 1.4m from A and 0.8m from B. Find the modulus of elasticity of the strings.
I'm having a bit of trouble with modelling the question with a diagram. I know what the correct answer is, and the model needed to help solve it (1) (bear in mind I've omitted some info to draw them faster), but I thought (2) will also be valid, just using the extension of the string at B as 0.05 instead of using Pythagoras' theorem.
Why not 2?
(2) is not valid. The reason is that (2) is not an equilibrium case. The string to $A$ has a horizontal component of the elastic force. In order to be in equilibrium, the elastic force of the string to $B$ has to have the horizontal component of the same magnitude, in opposite direction