If the resultant of `n` forces of different magnitudes acting at a point is zero, then the minimum value of `n` is

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To solve the problem, we need to determine the minimum number of forces \( n \) that can act at a point such that their resultant is zero, given that the forces have different magnitudes.

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to find the minimum number of forces acting at a point such that their vector sum is zero. The forces must have different magnitudes.

2. **Considering Two Forces**: Let's first analyze the case when \( n = 2 \). If we have two forces \( F_1 \) and \( F_2 \) acting at an angle to each other, for them to balance each other, they would need to be equal in magnitude and opposite in direction. However, since the problem states that the forces have different magnitudes, two forces cannot balance each other. Thus, \( n = 2 \) is not sufficient.

- **Hint**: Think about how two forces can balance each other. What happens if they have different magnitudes?

3. **Considering Three Forces**: Now, let's analyze the case when \( n = 3 \). We can arrange three forces \( F_1 \), \( F_2 \), and \( F_3 \) such that they can form a closed triangle. For the forces to balance, the following conditions must hold:
- The horizontal components of the forces must sum to zero.
- The vertical components of the forces must also sum to zero.

This can be achieved if we position the forces appropriately. For example, if we have \( F_1 \) acting horizontally, we can have \( F_2 \) and \( F_3 \) acting at angles such that their components balance \( F_1 \) and each other.

- **Hint**: Consider how three vectors can be arranged to form a closed triangle. What conditions must be satisfied for them to balance?

4. **Conclusion**: Since \( n = 2 \) is not sufficient, but \( n = 3 \) can be arranged to balance each other, we conclude that the minimum value of \( n \) for which the resultant of the forces is zero is:

\[ \boxed{3} \]