Final answer:
The tension in the diagonal string can be found by using the equilibrium equation and eliminating one of the tensions.
Step-by-step explanation:
In this question, we are given the equilibrium equation for the x-direction, which tells us that the tension T₁ in the 5.0-cm string is twice the tension T₂ in the 10.0-cm string. Therefore, the shorter string will snap. By using the first equation to eliminate T₂ from the second equation, we can obtain the relation between the mass m on the pan and the tension T₁ in the shorter string.