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 step by step, we need to analyze the situation of a man carrying a load of 5 kg through a distance of 10 m in different scenarios. The question asks for the condition under which the minimum amount of work is done.

### Step 1: Understand the Concept of Work
Work is defined as the product of the force applied and the displacement in the direction of the force. Mathematically, it can be expressed as:
\[ W = F \cdot s \cdot \cos(\theta) \]
where:
- \( W \) is the work done,
- \( F \) is the force applied,
- \( s \) is the displacement,
- \( \theta \) is the angle between the force and the direction of displacement.

### Step 2: Analyze the Different Scenarios
1. **Moving Up an Incline Plane**: The angle \( \theta \) is less than 90 degrees, so \( \cos(\theta) \) is positive. Work done is positive but not minimum.
2. **Moving Down an Incline Plane**: Similar to moving up, the angle \( \theta \) is less than 90 degrees, resulting in positive work done.
3. **Moving Over a Horizontal Surface**: The angle \( \theta \) is 90 degrees. Therefore, \( \cos(90^\circ) = 0 \). This means:
\[ W = F \cdot s \cdot 0 = 0 \]
Hence, no work is done in this case.
4. **Lifting Vertically Upward**: The angle \( \theta \) is 0 degrees, so \( \cos(0^\circ) = 1 \). The work done is maximum in this case since the force is fully in the direction of displacement.

### Step 3: Conclusion
From the analysis, the scenario in which the minimum amount of work is done occurs when the man moves the load over a horizontal surface. In this case, the work done is zero.

### Final Answer
The minimum amount of work is done when he moves it over a horizontal surface.

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