What is the relationship mechanical advantage (MA) velocity Ratio (V.R) and efficiency with percentage?

1. Analyze the question The question asks for the relationship between mechanical advantage (M.A), velocity ratio (V.R) and efficiency (expressed as a percentage) for a machine.

2. Concept

• Mechanical advantage (M.A) = Load ÷ Effort
• Velocity ratio (V.R) = Distance moved by effort ÷ Distance moved by load
• Efficiency = (Work output ÷ Work input) × 100%

3. Solution Work output = Load × distance moved by load Work input = Effort × distance moved by effort

Efficiency = (Load × load distance) / (Effort × effort distance) × 100%

Rearranging:

Efficiency = (Load/Effort) ÷ (effort distance/load distance) × 100%

Efficiency = (M.A / V.R) × 100%

Checking the options:

• A. e = M.A/V.R × 100% ✔ This matches the derivation.
• B. M.A = E.V.R is incomplete as written. Without the 100% factor it only works if E is a fraction, and it is not the standard percentage form.
• C. V.R = 1 ÷ sin θ is the velocity ratio of an inclined plane, not the general relationship.
• D. M.A = 1/E × 100% is wrong dimensionally and conceptually.

4. Answer

5. Exam tip Remember it as "M.A over V.R, times 100." Efficiency is always less than 100% for real machines, so M.A is always less than V.R. If an option gives M.A > V.R, eliminate it immediately.