Machines — identify the incorrect statement: Which of the following statements about friction, efficiency, mechanical advantage, and velocity ratio is incorrect?

Introduction / Context:
Basic machine parameters—mechanical advantage (M.A.), velocity ratio (V.R.), and efficiency—are frequently confused in exams. This question asks you to spot the incorrect statement among commonly paired definitions.

Given Data / Assumptions:

• M.A. = Load / Effort.
• V.R. = Distance moved by effort / Distance moved by load (for the same time interval).
• Efficiency η = M.A. / V.R.
• Limiting friction and normal reaction are standard in dry friction theory.

Concept / Approach:
Check each statement against standard definitions. Friction indeed opposes relative motion. Coefficient of friction μ = Limiting friction / Normal reaction. An ideal machine has η = 100% (no losses). V.R., however, is a kinematic ratio of distances or velocities, not a force ratio; the force ratio is M.A.

Step-by-Step Solution:
Evaluate (a): definition of friction — correct.Evaluate (b): μ = F_limiting / N — correct.Evaluate (c): ideal machine ⇒ η = 100% — correct.Evaluate (d): claims V.R. = Load / Effort (force ratio) — this is actually M.A. Hence (d) is incorrect.

Verification / Alternative check:
Consider a simple pulley: effort moves 2 m while load rises 1 m ⇒ V.R. = 2. If load is 100 N and effort is 60 N ⇒ M.A. = 100/60 ≈ 1.67 and η = 1.67/2 ≈ 83%. Distances vs forces clearly differ.

Why Other Options Are Wrong (i.e., why they are correct statements):

• (a) and (b) align with standard friction definitions.
• (c) defines the idealized, lossless machine correctly.

Common Pitfalls:

• Swapping M.A. and V.R. because both are ratios; remember V.R. is geometric/kinematic, M.A. is force-based.

Final Answer:
The velocity ratio of a machine is the ratio of load lifted to the effort applied.