What is the diameter of the rope used?

• A. 11 mm
• B. 9 mm
• C. 13 mm
• D. 10 mm

Answer: (A)

The important idea here is choosing a rope diameter that can safely carry the required load while still fitting in the given setup. A rope’s strength comes from its cross-sectional area, and that area is tied to the allowable stress of the material. So you determine the minimum area needed to carry the load with an adequate safety margin, then convert that area to a diameter using A = π(d/2)^2. In practice, you compare standard rope sizes and pick the smallest diameter that meets the load requirement and also fits inside the drum, guides, or other hardware.

In this problem, that means selecting the diameter that is just large enough to handle the load safely but not so large that it won’t fit. The other options are either too weak for the load or too bulky to fit, so the chosen diameter is the one that satisfies both conditions. When solving, you’d compute the required diameter from the load and material strength, then pick the smallest standard size that meets or exceeds that value while fitting the apparatus.