Efficiency of a lifting machine — definitions and equivalent forms The efficiency of a lifting machine is defined as which of the following?

Introduction / Context:
Machine efficiency quantifies how effectively a device converts input work into useful output. Recognizing equivalent definitions helps connect kinematic and force-based viewpoints (velocity ratio vs. mechanical advantage).

Given Data / Assumptions:

• Efficiency η is a dimensionless ratio lying between 0 and 1 for real machines.
• Mechanical Advantage (M.A.) = Load / Effort.
• Velocity Ratio (V.R.) = distance moved by effort / distance moved by load.

Concept / Approach:
By definition, η = output / input = useful work out / work in. Using M.A. and V.R., it can be shown that η = M.A. / V.R. because Work = Force * Distance, so (Load * load distance) / (Effort * effort distance) = (Load/Effort) / (effort distance/load distance) = M.A. / V.R.

Step-by-Step Solution:

Verification / Alternative check:
For an ideal machine (η = 1), M.A. = V.R. — a standard consistency check used in exam problems.

Why Other Options Are Wrong:

• Options A, B, and C are all correct forms of the same concept; therefore, the combined choice “All of the above” is correct.
• “Velocity ratio to mechanical advantage” inverts the correct relation and would give values greater than 1 for ideal machines, which is not the standard convention.

Common Pitfalls:
Confusing efficiency with M.A. itself; overlooking distances when comparing forces; forgetting that η cannot exceed 1 for real machines.

Final Answer:
All of the above