How is mechanical advantage related to velocity ratio for (i) an ideal machine, (ii) a practical machine ?

Answer

To solve the question regarding the relationship between mechanical advantage and velocity ratio for both ideal and practical machines, we can break it down into the following steps:

### Step-by-Step Solution:

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

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 can be expressed as:
\[ VR = \frac{\text{Distance moved by Effort}}{\text{Distance moved by Load}} \]

3. **Relationship for an Ideal Machine**:
- In an ideal machine, there are no losses due to friction or other factors. Therefore, the mechanical advantage is equal to the velocity ratio.
- This can be stated as:
\[ MA = VR \quad \text{(for an ideal machine)} \]

4. **Relationship for a Practical Machine**:
- In a practical machine, there are losses due to friction, deformation, and other factors. As a result, the mechanical advantage is always less than the velocity ratio.
- This can be expressed as:
\[ MA < VR \quad \text{(for a practical machine)} \]
- This inequality arises because the efficiency of a practical machine is less than one.

5. **Conclusion**:
- To summarize, for an ideal machine, the mechanical advantage equals the velocity ratio, while for a practical machine, the mechanical advantage is less than the velocity ratio due to inefficiencies.