Systems of Pulleys – Second System (Weston-type) Velocity Ratio In the second system of pulleys comprising n pulleys, the velocity ratio (VR) is claimed to be n. Is this statement correct?

Introduction / Context: Pulleys are classic simple machines used to gain mechanical advantage. There are three traditional “systems of pulleys.” Each system has a distinct expression for velocity ratio (VR), which relates effort movement to load movement. Misremembering which VR belongs to which system is a common exam error.

Given Data / Assumptions:

• Second system of pulleys with n pulleys.
• Light, inextensible rope; ideal kinematics for VR (independent of friction).

Concept / Approach: For the three classical systems: First system: VR = 2^n. Second system: VR = 2^n − 1. Third system: VR = n. The claim “VR = n” therefore pertains to the third system, not the second.

Step-by-Step Solution: Identify the system: it is the second system. Recall standard formula: VR_second = 2^n − 1. Compare with claim VR = n ⇒ mismatch. Hence the statement is false.

Verification / Alternative check: For n = 3: second system VR = 2^3 − 1 = 7. If one incorrectly used n, VR would be 3, which clearly contradicts textbook results and simple rope-segment counting.

Why Other Options Are Wrong: “True”: incorrect; VR = n belongs to the third system. “True only if massless/frictionless”: VR formulas already assume ideal kinematics; friction affects efficiency, not VR. “True when n = 2”: still wrong; for n = 2, VR = 3 (not 2). “True for first system”: first system has 2^n, not n.

Common Pitfalls: Mixing up the three systems’ formulas. Confusing velocity ratio (a kinematic quantity) with mechanical advantage (a force ratio affected by friction).

Final Answer: False