`21` 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 coplanar non-collinear forces that maintain a body in equilibrium, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**: We have 21 coplanar forces acting on a body, all of equal magnitude, and they maintain the body in equilibrium. Since they are in equilibrium, the resultant of all these forces must be zero.

2. **Closed Polygon Representation**: Since the forces are of equal magnitude and are acting in different directions, they can be represented as the sides of a closed polygon. The number of sides of this polygon will be equal to the number of forces, which is 21.

3. **Calculating the Central Angle**: For a polygon with \( n \) sides, the angle at the center corresponding to each side (or force) is given by the formula:
\[ \text{Central Angle} = \frac{360^\circ}{n} \]
In our case, \( n = 21 \). Therefore, the central angle will be:
\[ \text{Central Angle} = \frac{360^\circ}{21} = 17.14^\circ \]

4. **Angle Between Adjacent Forces**: The angle between any two adjacent forces is equal to the central angle calculated above. Thus, the angle between any two adjacent forces is:
\[ \text{Angle between adjacent forces} = 17.14^\circ \]

### Final Answer:
The angle between any two adjacent forces is approximately \( 17.14^\circ \).

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