`12` coplanar non collinear forces (all of equal magnitude) maintain a body in equilibrium, then angle between any two adjacent forces is

Options

A. `15^(@)`
B. `30^(@)`
C. `45^(@)`
D. `60^(@)`

Explanation

To solve the problem, we need to determine the angle between any two adjacent forces when 12 coplanar non-collinear forces of equal magnitude maintain a body in equilibrium.

### Step-by-Step Solution:

1. **Understanding Equilibrium**:
- When a body is in equilibrium, the net force acting on it is zero. This means that the vector sum of all the forces must cancel each other out.

2. **Identifying the Forces**:
- We have 12 coplanar non-collinear forces. Since they are non-collinear, they cannot all act along the same line. Instead, they must be arranged in such a way that they form a closed shape (polygon).

3. **Forming a Closed Polygon**:
- For the body to be in equilibrium with these 12 forces, they must form a closed polygon with 12 sides. Each force can be represented as a side of the polygon.

4. **Calculating the Angle**:
- The total angle around a point is 360 degrees. If we have a polygon with \( n \) sides, the angle subtended at the center by each side (or force) can be calculated using the formula:
\[ \text{Angle} = \frac{360^\circ}{n} \]
- Here, \( n = 12 \) (the number of forces).

5. **Substituting the Value**:
- Substituting \( n = 12 \) into the formula gives:
\[ \text{Angle} = \frac{360^\circ}{12} = 30^\circ \]

6. **Conclusion**:
- Therefore, the angle between any two adjacent forces is \( 30^\circ \).

### Final Answer:
The angle between any two adjacent forces is \( 30^\circ \).

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