It is not sufficient to maintain an equilibrium that forces balance in each direction. There must also be no turning force about any point. The following diagram shows a non - uniform rod of weight 100 N held horizontal by tensions
and
in cables attached to either end of the rod.
The centre of gravity of the rod is a distance x froim end A.
Resolving vertically gives
Subtracting these, and using that
gives
Then
Taking moments about A gives