Machines — Differential Pulley Block A differential pulley block has effort pulley diameters of 100 mm (larger) and 80 mm (smaller). What is its velocity ratio (VR)?

Introduction / Context:
Differential (Weston) pulley blocks are simple lifting machines used to gain mechanical advantage. The velocity ratio (VR) links the distance moved by the effort to the distance moved by the load, and it depends on the diameters (or radii) of the two effort pulleys.

Given Data / Assumptions:

• Larger pulley diameter D = 100 mm.
• Smaller pulley diameter d = 80 mm.
• Standard ideal relation for Weston differential pulley: VR = 2D / (D - d) when diameters are used.

Concept / Approach:
For a Weston differential pulley, the chain passes over two co-axial pulleys of slightly different diameters. One revolution advances one side and retracts the other, creating a small net movement of the load. Thus VR grows as the difference (D - d) becomes small, per the formula VR = 2D / (D - d).

Step-by-Step Solution:

Verification / Alternative check:
Using radii R and r (R = 50 mm, r = 40 mm) gives VR = 2R / (R - r) = 100 / 10 = 10, consistent with the diameter-based calculation.

Why Other Options Are Wrong:
5, 20, and 40 do not satisfy the standard relation for the given diameters; they would require different D and d values or a different machine type.

Common Pitfalls:
Mixing up the formula with simple pulley systems; forgetting the factor of 2; using (D + d) instead of (D - d).

Final Answer:
10.