Which of the following relations is correct?

Options

A. Mechanical advantage = Effort/Load
B. Load arm `xx` Effort = Effort arm `xx` Load
C. Load arm `xx` Load = Effort arm `xx` Effort
D. None of these

Explanation

To determine which of the given relations is correct, we need to analyze the concepts of mechanical advantage and the relationships between load, effort, load arm, and effort arm in a system of particles.

### Step-by-Step Solution:

1. **Understanding the System**:
- We are dealing with a lever system where there are two masses: a load (the weight being lifted) and an effort (the force applied to lift the load).
- The lever has two arms: the load arm (distance from the fulcrum to the load) and the effort arm (distance from the fulcrum to the point where the effort is applied).

2. **Mechanical Advantage (MA)**:
- The mechanical advantage of a lever is defined as the ratio of the load to the effort.
- Mathematically, it is expressed as:
\[ \text{Mechanical Advantage (MA)} = \frac{\text{Load}}{\text{Effort}} \]

3. **Lever Principle**:
- According to the principle of moments (or the law of the lever), for a lever in equilibrium, the moments about the fulcrum must be equal. This can be expressed as:
\[ \text{Load} \times \text{Load Arm} = \text{Effort} \times \text{Effort Arm} \]

4. **Analyzing the Given Relations**:
- We need to evaluate the given options based on the principles outlined above.
- If any of the options contradict the principle of moments or the definition of mechanical advantage, they are incorrect.

5. **Identifying the Correct Relation**:
- From our analysis, the correct relation that holds true for a lever in equilibrium is:
\[ \text{Load} \times \text{Load Arm} = \text{Effort} \times \text{Effort Arm} \]
- This means that if the relation given in the options matches this equation, it is correct.

6. **Conclusion**:
- After evaluating all the options, we find that option C is the correct relation. Options A, B, and D do not satisfy the conditions of equilibrium or the definition of mechanical advantage.

### Final Answer:
The correct answer is **Option C**.