A body is moved through a distance of 5 m in the following different ways. Maximum work is done when the body is

Options

A. pushed over an inclined plane
B. raised vertically upwards
C. pushed over smooth rollers
D. pushed on a plane horizontal surface

Answer

To determine when maximum work is done while moving a body through a distance of 5 meters, we need to understand the concept of work in physics. Work is defined as the product of the force applied to an object and the distance over which that force is applied, in the direction of the force. The formula for work (W) is given by:

\[ W = F \cdot d \cdot \cos(\theta) \]

Where:
- \( W \) = Work done
- \( F \) = Force applied
- \( d \) = Distance moved (5 m in this case)
- \( \theta \) = Angle between the force and the direction of motion

### Step-by-Step Solution:

1. **Identify the Scenarios**: We need to analyze the different ways the body can be moved through 5 meters. The options typically include:
- Moving horizontally
- Moving vertically
- Moving along an inclined plane
- Moving in a circular path

2. **Calculate Work Done in Each Scenario**:
- **Horizontal Movement**: If the body is moved horizontally, the angle \( \theta \) is 0 degrees. Thus, \( \cos(0) = 1 \).
\[ W = F \cdot 5 \cdot 1 = 5F \]
- **Vertical Movement**: If the body is lifted vertically, the angle \( \theta \) is 90 degrees. Thus, \( \cos(90) = 0 \).
\[ W = F \cdot 5 \cdot 0 = 0 \]
- **Inclined Plane**: If the body is moved up an inclined plane, the angle \( \theta \) will be between 0 and 90 degrees. The force required will be less than the weight of the body, and \( \cos(\theta) \) will be less than 1, leading to less work done compared to horizontal movement.
- **Circular Path**: If the body moves in a circular path, the angle between the force (centripetal force) and the direction of motion is also 90 degrees, resulting in no work done.
\[ W = F \cdot 5 \cdot 0 = 0 \]

3. **Compare the Work Done**:
- Horizontal movement yields the maximum work done as it utilizes the full force applied in the direction of motion.
- Vertical movement, inclined plane movement, and circular movement yield lesser or no work done.

4. **Conclusion**: The maximum work is done when the body is moved horizontally through a distance of 5 meters.

### Final Answer:
Maximum work is done when the body is moved horizontally through a distance of 5 meters.