Which of the following statements is/are correct in any machine? I. The velocity ratio is usually greater than…

Analyzing the question

We need to decide which of three statements about machines are correct.

Concepts

• Mechanical advantage (MA) = Load / Effort
• Velocity ratio (VR) = distance moved by effort / distance moved by load
• Efficiency = (MA / VR) × 100% = (work output / work input) × 100%

Checking each statement

I. VR is usually greater than MA. Efficiency = MA/VR is less than 1 for real machines because of friction and the weight of moving parts. So MA < VR, which means VR is usually greater than MA. Correct.

II. Efficiency = work input / work output (as the question is written, "work input" over "work output"). The correct definition is efficiency = work output / work input. The statement as printed appears to be the inverse, or at best is garbled. The wording in the question is ambiguous, but it is read as the reverse of the true definition. Taken that way, it is incorrect. Also, the true ratio would be greater than 1 if it were inverted, which is impossible for efficiency.

III. VR is independent of friction. VR depends only on the geometry of the machine (distances moved, number of pulley strands, radii of gears, etc.). Friction affects the effort needed, so it affects MA, but not VR. Correct.

Conclusion Statements I and III are correct.

Tip: Remember "VR is geometry, MA is reality." VR is fixed by the design of the machine, while MA drops when friction rises. Also, always check that efficiency is output over input, never the other way round, since efficiency can never exceed 100%.