In a single movable pulley, if the effort moves by a distance x upwards, by what height is the load raised ?

Answer

To solve the problem of how much height the load is raised in a single movable pulley when the effort moves a distance \( x \) upwards, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Pulley System**: In a single movable pulley system, the pulley is attached to the load, and the effort is applied on one side of the rope that goes over the pulley.

2. **Movement of the Effort**: When the effort moves upwards by a distance \( x \), it pulls the rope attached to the movable pulley.

3. **Effect on the Load**: The movable pulley effectively doubles the distance that the load is raised compared to the distance the effort moves. This is because for every unit of distance the effort moves, the load moves half that distance due to the configuration of the pulley.

4. **Calculating the Height Raised**: Therefore, if the effort moves upwards by a distance \( x \), the load will be raised by:
\[ \text{Height raised by the load} = \frac{x}{2} \]

5. **Final Answer**: Thus, the height by which the load is raised when the effort moves by a distance \( x \) upwards is:
\[ \text{Height raised} = \frac{x}{2} \]

### Summary:
When the effort moves a distance \( x \) upwards, the load is raised by \( \frac{x}{2} \).