Draw a diagram of a combination of three movable pulleys and one fixed pulley to lift up a load. In the diagram, show the directions of load, effort and tension in each strand. Find : (i) the mechanical advantage, (ii) the velocity ratio, and (iii) the efficiency of the combination, in the ideal situation.

Answer

### Step-by-Step Solution

1. **Draw the Diagram**:
- Start by sketching a fixed pulley (D) at the top.
- Below it, draw three movable pulleys (A, B, and C) in a vertical arrangement.
- Connect the pulleys with ropes, ensuring that the load (L) is attached to the last movable pulley (C).
- Indicate the direction of the load (downward), effort (downward), and tension (upward) in each strand of the rope.

**Hint**: Remember that the fixed pulley changes the direction of the effort, while the movable pulleys help in lifting the load.

2. **Identify the Load and Tensions**:
- From the diagram, the load (L) is equal to the sum of two tensions (T1) acting upwards on the first movable pulley (A).
- Therefore, \( L = 2T_1 \).

**Hint**: The load is supported by the tensions in the rope, so visualize how the pulleys distribute the load.

3. **Calculate Tension Relationships**:
- For the second movable pulley (B), the tension \( T_1 \) is equal to the sum of two tensions \( T_2 \):
\[ T_1 = 2T_2 \implies T_2 = \frac{T_1}{2} \]
- For the third movable pulley (C), the tension \( T_2 \) is equal to the sum of two tensions \( T_3 \):
\[ T_2 = 2T_3 \implies T_3 = \frac{T_2}{2} \]

**Hint**: Each movable pulley effectively halves the tension in the rope as you move down the system.

4. **Substitute Tension Values**:
- Substitute \( T_2 \) into the equation for \( T_3 \):
\[ T_3 = \frac{T_1}{4} \]
- Substitute \( T_1 \) from the load equation:
\[ T_3 = \frac{L}{4} \]

**Hint**: Keep track of how each tension relates to the load as you substitute values.

5. **Determine Mechanical Advantage (MA)**:
- The mechanical advantage is defined as the ratio of load to effort:
\[ MA = \frac{L}{T_3} = \frac{L}{\frac{L}{4}} = 4 \]

**Hint**: Mechanical advantage tells you how many times the effort is reduced by the pulley system.

6. **Calculate Velocity Ratio (VR)**:
- The velocity ratio is the ratio of the distance moved by the effort to the distance moved by the load. For this system:
\[ VR = 2^3 = 8 \]

**Hint**: Velocity ratio indicates how much farther the effort moves compared to the load.

7. **Find Efficiency**:
- Efficiency is the ratio of mechanical advantage to velocity ratio:
\[ Efficiency = \frac{MA}{VR} = \frac{4}{8} = 0.5 \text{ or } 50\% \]

**Hint**: Efficiency shows the effectiveness of the machine; in an ideal situation, it should be 100%, but here it's 50% due to the nature of the system.

### Summary of Results
- **Mechanical Advantage (MA)**: 4
- **Velocity Ratio (VR)**: 8
- **Efficiency**: 50%