# Mininizing tension

A heavy horizontal girder of length $$L$$ has several objects hung from it.It is supported by a frictionless pivot at one end and a cable of neglegible weight that is attached to a I beam, at a point directly above girder's center at height $$H$$. Where should the other end of the cable be attached to the girder so that the cable’s tension is minimum (Hint: In evaluating and presenting your answer, don’t forget that the maximum distance of the point of attachment from the pivot is the length$$L$$ of the beam.)?

The answer can be expressed as $$\dfrac{p}{q}.H^x.L^y$$

Find $$p+q+x+y$$

Note

• $$p,q$$ are coprime.
• what could be the case if $$h \leq \dfrac{L}{2}$$