How is mechanical advantage related with velocity ratio for an actual machine ? State whether the efficiency of such a machine is equal to 1, les sthan 1 or more than 1.

Answer

To solve the question regarding the relationship between mechanical advantage (MA) and velocity ratio (VR) for an actual machine, as well as the efficiency of such a machine, we can follow these steps:

### Step-by-Step Solution:

1. **Define Mechanical Advantage (MA)**:
- Mechanical Advantage is defined as the ratio of the load force (output force) to the effort force (input force) in a machine. It indicates how much the machine amplifies the input force.

\[ MA = \frac{\text{Load}}{\text{Effort}} \]

2. **Define Velocity Ratio (VR)**:
- Velocity Ratio is defined as the ratio of the distance moved by the effort to the distance moved by the load. It indicates how much the machine changes the distance moved by the effort compared to the load.

\[ VR = \frac{\text{Distance moved by Effort}}{\text{Distance moved by Load}} \]

3. **Relationship Between MA and VR**:
- For an actual machine, the relationship between Mechanical Advantage and Velocity Ratio is given by the formula:

\[ MA = \text{Efficiency} \times VR \]

Where Efficiency (η) is a measure of how effectively the machine converts input energy into output work.

4. **Understanding Efficiency**:
- Efficiency is defined as the ratio of useful work output to the total work input, and it is expressed as a decimal or percentage.

\[ \text{Efficiency} = \frac{\text{Useful Work Output}}{\text{Total Work Input}} \]

5. **Efficiency of Actual Machines**:
- In real-world applications, due to factors like friction, wear, and other losses, the efficiency of an actual machine is always less than 1 (or 100%).
- Therefore, we can conclude that:

\[ \text{Efficiency} < 1 \]

### Conclusion:
- The relationship between mechanical advantage and velocity ratio for an actual machine is given by \( MA = \text{Efficiency} \times VR \).
- The efficiency of such a machine is always less than 1.