`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 of finding the angle between any two adjacent forces when 12 coplanar non-collinear forces of equal magnitude maintain a body in equilibrium, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Forces**: We have 12 coplanar non-collinear forces acting on a body, all of equal magnitude, which means they can be represented as vectors of the same length.

2. **Use the Polygon Law of Vector Addition**: According to the polygon law of vector addition, if multiple forces (vectors) are acting on a body and the body is in equilibrium, these forces can be represented as the sides of a polygon. The resultant force is represented by the closing side of the polygon.

3. **Determine the Number of Forces**: In this case, we have \( n = 12 \) forces. The forces will form a closed polygon, where each force represents a side of the polygon.

4. **Calculate the Interior Angles**: The sum of the interior angles of a polygon with \( n \) sides is given by the formula:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
For \( n = 12 \):
\[ \text{Sum of interior angles} = (12 - 2) \times 180^\circ = 10 \times 180^\circ = 1800^\circ \]

5. **Find the Angle Between Adjacent Forces**: The angle between any two adjacent forces (or sides of the polygon) can be found by dividing the total sum of the interior angles by the number of sides (forces):
\[ \text{Angle between adjacent forces} = \frac{\text{Sum of interior angles}}{n} = \frac{1800^\circ}{12} = 150^\circ \]

6. **Calculate the Angle Between Adjacent Forces**: However, since we are looking for the angle between adjacent forces in a circular arrangement, we can also use the formula:
\[ \theta = \frac{360^\circ}{n} \]
Substituting \( n = 12 \):
\[ \theta = \frac{360^\circ}{12} = 30^\circ \]

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