Question

12 coplanar non collinear forces (all of equal magnitude) maintain a body in equilibrium, then the angle between any two adjacent forces is:
(A). ${{15}^{\circ }}$
(B). \[{{30}^{\circ }}\]
(C). ${{45}^{\circ }}$
(D). ${{60}^{\circ }}$

Answer 1

- Hint: Coplanar forces, means all the 12 forces are lying in the same plane. Non collinear forces means the forces are not lying or acting in the same straight line.

Complete step-by-step solution -

Polygon law of vector addition states that when a number of vectors in space are represented as the sides of a polygon in magnitude and direction, taken in the same order, then the resultant vector is represented by the closing side of that polygon taken in the opposite order.
According to the polygon law of vector addition, the 11 forces will be the sides of the polygon in the same order in direction and 1 force will represent the resultant which is a side in the opposite order of the polygon.
Now, we know that for every polygon, the sum of interior angles of a polygon is equal to 360$^{\circ }$ irrespective of the number of sides of the polygon.
So, the required angle is equal to
$\begin{align}
  & \to \dfrac{{{360}^{\circ }}}{n} \\
 & \to \dfrac{{{360}^{\circ }}}{12} \\
 & \to {{30}^{\circ }} \\
\end{align}$
Hence, angle between any two adjacent forces is ${{30}^{\circ }}$

Additional information:
A resultant vector is defined as a single vector whose effect is the same as the combined effect of two or more vectors.
Vector addition follows Additive law and Commutative law.

Note:- The vectors to be added should have the same nature, i.e. force can be added to force and velocity can be added to velocity, but the force cannot be added to the velocity.
Scalars and vectors can never be added.