The minimum number of unequal forces in a plane that can keep a particle in equilibrium is

Options

A. 4
B. 2
C. 3
D. 6

Answer

To solve the problem of determining the minimum number of unequal forces in a plane that can keep a particle in equilibrium, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Equilibrium**:
A particle is in equilibrium when the net force acting on it is zero. This means that all the forces acting on the particle must balance each other out.

2. **Considering Forces**:
Let's denote the forces acting on the particle as \( F_1, F_2, \) and \( F_3 \). For the particle to be in equilibrium, the vector sum of these forces must equal zero:
\[ F_1 + F_2 + F_3 = 0 \]

3. **Using Two Forces**:
If we consider two forces, say \( F_2 \) and \( F_3 \), they can be equal in magnitude but opposite in direction to balance \( F_1 \). However, the question specifies that the forces must be unequal.

4. **Applying Three Forces**:
To satisfy the condition of having unequal forces while still achieving equilibrium, we can apply one force \( F_1 \) and two other forces \( F_2 \) and \( F_3 \) such that:
\[ F_1 = F_2 + F_3 \]
Here, \( F_2 \) and \( F_3 \) must be unequal in magnitude but their vector sum must equal \( F_1 \).

5. **Conclusion**:
Therefore, the minimum number of unequal forces required to keep a particle in equilibrium is three.

### Final Answer:
The minimum number of unequal forces in a plane that can keep a particle in equilibrium is **three**.

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