A man carries a load of 5 kg on his head through a distance of 10 m. the minimum amount of work is done when he

Options

A. Move it up an inclined plane
B. Moves it down an inclined plane
C. Moves it over a horizontal surface
D. Lifts it vertically upwards.

Answer

To solve the problem, we need to understand the concept of work done in physics. Work done (W) is defined as the product of the force (F) applied to an object and the distance (d) over which that force is applied, in the direction of the force. Mathematically, it can be expressed as:

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

where:
- \( W \) is the work done,
- \( F \) is the force applied,
- \( d \) is the distance moved,
- \( \theta \) is the angle between the force and the direction of motion.

### Step-by-Step Solution:

1. **Identify the Weight of the Load**:
The load carried by the man is 5 kg. The weight (force due to gravity) can be calculated using the formula:
\[ F = m \cdot g \]
where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).
\[ F = 5 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 49.05 \, \text{N} \]

2. **Consider Different Scenarios**:
- **Moving Up an Incline**: The force exerted is against gravity, and the angle \( \theta \) is not zero, resulting in more work done.
- **Moving Down an Incline**: The force of gravity assists the movement, reducing the effective force needed to move the load, hence minimizing work done.
- **Moving Over a Horizontal Surface**: The force of gravity acts downward, but the movement is horizontal, resulting in a \( \theta \) of 90 degrees, which means no work is done against gravity.
- **Lifting Vertically Upwards**: The entire weight must be lifted against gravity, resulting in maximum work done.

3. **Determine the Minimum Work Done**:
The minimum work is done when the man moves the load down an incline. In this case, the gravitational force assists the movement, and the effective force required to move the load is reduced.

4. **Conclusion**:
Therefore, the minimum amount of work is done when the man moves the load down an incline.

### Final Answer:
The minimum amount of work is done when he **moves it down an incline plane**.