Systems of pulleys — identifying the system by velocity ratio: If, in a tackle, the number of pulleys is equal to the velocity ratio (V.R.), then the arrangement corresponds to which standard system of pulleys?

Introduction / Context:
Pulley systems are categorized (first, second, third) based on how pulleys are arranged and how many rope segments support the moving block. Velocity ratio (V.R.)—the ratio of distance moved by effort to distance moved by load—identifies the system and guides mechanical advantage estimates.

Given Data / Assumptions:

• The number of pulleys n equals the velocity ratio.
• Idealized ropes and pulleys (no slip, massless rope, friction neglected) for the identification rule of thumb.

Concept / Approach:
For the standard systems: First system yields V.R. = 2^m (m = pulleys in the moving block). Second system yields V.R. ≈ 2m (number of supporting segments). Third system yields V.R. ≈ n (numerically equal to the number of pulleys). Therefore, n = V.R. directly maps to the third system of pulleys.

Step-by-Step Solution:
Recall V.R. patterns: first → 2^m; second → 2m; third → n.Given n = V.R., this matches the third system.Hence, select “third.”

Verification / Alternative check:
Draw small examples: with 3 pulleys arranged in the third system, V.R. = 3; contrast with second system where 3 pulleys could give V.R. = 4, demonstrating non-equality to n.

Why Other Options Are Wrong:

• first / second: Their V.R. formulas do not equal the simple count of pulleys.

Common Pitfalls:

• Assuming mechanical advantage always equals V.R.; in real systems friction reduces M.A. below V.R.

Final Answer:
third