A man carries a load on his head through a distance of 5 m. The maximum amount of work is done when he

Options

A. Moves it over an inclined plane
B. Moves it over a horizontal surface
C. Lifts it vertically upwards
D. None of these

Answer

To solve the problem of determining when the maximum amount of work is done by a man carrying a load on his head through a distance of 5 meters, we can follow these steps:

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

### Step 2: Identify the Direction of Forces
In this scenario, the man carries a load on his head. The force he exerts (to counteract gravity) is directed vertically upwards. The gravitational force acting on the load is directed downwards.

### Step 3: Analyze the Displacement
The man is moving through a distance of 5 meters. We need to consider the direction of this displacement:
- If he moves horizontally, the displacement is horizontal, while the force is vertical. The angle \( \theta \) between the force and displacement is 90 degrees.
- If he lifts the load vertically upwards, both the force and displacement are in the same direction (upwards), making \( \theta = 0 \) degrees.

### Step 4: Calculate Work Done in Different Scenarios
1. **Horizontal Movement**:
- \( \theta = 90^\circ \)
- \( \cos(90^\circ) = 0 \)
- Work done \( W = F \cdot d \cdot 0 = 0 \)

2. **Vertical Movement**:
- \( \theta = 0^\circ \)
- \( \cos(0^\circ) = 1 \)
- Work done \( W = F \cdot d \cdot 1 = F \cdot d \)

### Step 5: Determine Maximum Work Done
From the calculations, we see that the work done is maximized when the force and displacement are in the same direction (i.e., when the man lifts the load vertically upwards). Therefore, the maximum amount of work is done when he lifts the load vertically.

### Conclusion
The correct answer is that the maximum amount of work is done when the man lifts the load vertically upwards.