A man starts walking from a point on the surface of earth (assumed smooth ) and reaches diagonally opposite point . What is the work done by him.

Options

A. Zero
B. Positive
C. Negative
D. Nothing can be said

Answer

To solve the problem of determining the work done by a man walking from one point on the surface of the Earth to a diagonally opposite point, we can follow these steps:

### Step 1: Understanding Work Done
The work done (W) by a force is defined as the product of the force (F) applied and the displacement (d) in the direction of the force. The formula for work done is:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \( \theta \) is the angle between the force and the direction of displacement.

### Step 2: Analyzing the Situation
In this scenario, the man is walking from one point to a diagonally opposite point on a smooth surface. The key point to note here is that while the man is moving, the total displacement from the starting point to the ending point must be considered.

### Step 3: Calculating Displacement
Displacement is defined as the change in position. If the man starts at point A and walks to point B, which is diagonally opposite, we can visualize this as moving across a straight line (the diagonal). However, since he returns to a point that is directly opposite to his starting point, the net displacement can be considered.

### Step 4: Displacement Calculation
If we denote the starting point as (0, 0) and the diagonally opposite point as (x, y), the displacement vector can be represented as:
\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} \]
Since he ends up at the diagonally opposite point, the displacement can be calculated as:
\[ \text{Displacement} = (x, y) - (0, 0) = (x, y) \]

However, if we consider the total path taken, the effective displacement in terms of the straight line distance is zero because he returns to the same level (ground level) after completing the journey.

### Step 5: Conclusion on Work Done
Since the man returns to the same vertical level and the net displacement vector from the starting point to the ending point is zero, the work done by the man is:
\[ W = F \cdot 0 = 0 \]
Thus, the total work done by the man while walking to the diagonally opposite point is zero.

### Final Answer
The work done by the man is **0 Joules**.

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