Final answer:
To find the tension in the cable with one equation, use the pivot point at the pan's attachment, which negates the tension's rotational effect due to zero distance from the pivot.
Step-by-step explanation:
To most easily find the tension in the cable using only one equation, the ideal pivot choice is the point where the cable is attached to the pan.
By choosing this pivot point, the rotational effect of the tension force would be zero because the distance from the pivot to the line of action of the tension force is zero. Consequently, any equations for torques (rotational effects) about the pivot would not include the tension, simplifying the problem.
Instead, we would only need the first condition for equilibrium. The remaining forces would be the weight of the pan, neglecting the weight of the strings, and the tension forces would be parallel to the strings' lengths, following Newton's third law. One can solve for the tension exerted by one string using the equilibrium equations without requiring consideration of rotational forces.