The correct relationship between mechanical advantage (M.A.) velocity ratio (V.R.) and efficiency `(eta)` is:

Options

A. `M.A.=etaxxV.R.`
B. `V.R.=etaxxM.A.`
C. `eta=M.A.xxV.R.`
D. none of these

Answer

To find the correct relationship between mechanical advantage (M.A.), velocity ratio (V.R.), and efficiency (η), we can follow these steps:

### Step 1: Understand the Definitions
- **Mechanical Advantage (M.A.)**: It is the ratio of the output force to the input force in a machine.
- **Velocity Ratio (V.R.)**: It is the ratio of the distance moved by the effort to the distance moved by the load.
- **Efficiency (η)**: It is the ratio of the mechanical advantage to the velocity ratio, usually expressed as a percentage.

### Step 2: Write the Formula for Efficiency
The efficiency (η) can be expressed mathematically as:
\[ \eta = \frac{M.A.}{V.R.} \]

### Step 3: Rearranging the Formula
To find the relationship between M.A., V.R., and η, we can rearrange the formula:
\[ M.A. = \eta \times V.R. \]

### Step 4: Conclusion
From the rearranged formula, we can conclude that the correct relationship is:
\[ \text{Mechanical Advantage (M.A.)} = \text{Efficiency (η)} \times \text{Velocity Ratio (V.R.)} \]

### Final Answer
The correct relationship between mechanical advantage (M.A.), velocity ratio (V.R.), and efficiency (η) is:
\[ M.A. = \eta \times V.R. \]

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