Mechanical advantage being a ..... ratio is an............ quantity.

Options

A. cute, impure.
B. pure, irregular
C. pure, unitless
D. impure, measurable.

Explanation

To solve the question "Mechanical advantage being a ..... ratio is an............ quantity," we need to analyze the concept of mechanical advantage in physics.

### Step-by-step Solution:

1. **Understanding Mechanical Advantage**:
- Mechanical advantage (MA) is defined as the ratio of the load (output force) to the effort (input force) applied in a machine.
- Mathematically, it is expressed as:
\[ MA = \frac{\text{Load}}{\text{Effort}} \]

2. **Identifying the Type of Ratio**:
- Since both load and effort are forces, the mechanical advantage is a ratio of two forces.
- Ratios are often described as "pure" when they are dimensionless, meaning they do not have any units associated with them.

3. **Analyzing Dimensions**:
- The dimension of force is given by \( [F] = [M][L][T^{-2}] \) (mass × acceleration).
- Therefore, the dimensions of load and effort are the same, which means:
\[ [\text{Load}] = [\text{Effort}] = [F] = [M][L][T^{-2}] \]

4. **Calculating the Dimension of Mechanical Advantage**:
- When we take the ratio of load to effort, the dimensions cancel out:
\[ MA = \frac{[F]}{[F]} = \frac{[M][L][T^{-2}]}{[M][L][T^{-2}]} = 1 \]
- This shows that mechanical advantage has no dimensions.

5. **Conclusion**:
- Since mechanical advantage is a ratio of two forces that cancel each other out, it is a dimensionless quantity.
- Therefore, we can fill in the blanks in the question:
- "Mechanical advantage being a **pure** ratio is a **dimensionless** quantity."

### Final Answer:
Mechanical advantage being a **pure** ratio is a **dimensionless** quantity.

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