Final answer:
To find the tensions T1 and T2, we must apply static equilibrium conditions. The mass given and angle are used to resolve tensions into components. Additional details regarding string lengths and angles are needed for precise calculations.
Step-by-step explanation:
To solve for the tensions T1 and T2 in a state of static equilibrium, we assume that the object is suspended and at rest, meaning the sum of the forces in both the x and y directions must be zero. The system's equilibrium involves calculating the tension forces in the strings that are at an angle to the vertical. We know the mass of the object is 35kg, and the angle θ is 20°, which helps in resolving the tension forces into their x and y components. From the statement that the tension T1 in the 5.0-cm string is twice the tension T2 in the 10.0-cm string, we use trigonometry to split the tensions into components, apply Newton's first law for equilibrium (Σ F = 0), and solve for the individual tensions.
The problem does not provide all the necessary details for complete solution, such as the specific angles the strings make with the horizontal or their lengths, so remember to clarify these aspects before proceeding with the exact calculations.