Question

Three concurrent forces of the same magnitude are in equilibrium. What is the angle between the force? Also, name the triangle formed by the forces as sides

• A. $60°$ equilateral triangle
• B. $120°$ equilateral triangle
• C. $120°,30°,30°$ an isosceles triangle
• D. $120°$ an obtuse-angled triangle

Answer 1

The correct option is B

$120°$ equilateral triangle

Lami's theorem:

1. It asserts that each force is proportionate to the sine of the angle formed by the other two forces when three forces acting at a place are in equilibrium.
2. Consider the interaction of three forces $F_A,F_B,$ and $F_C$ on a particle or rigid body at angles $\alpha ,\beta ,$ and $\gamma$.

Therefore, $\frac{F_A}{\sin \alpha }=\frac{F_B}{\sin \beta }=\frac{F_C}{\sin \gamma }$.

Explanation:

1. The angle between the three contemporaneous forces is equal to $\frac{360}{3}=120.$ because they are all equal in magnitude and in balance.
2. The triangle will be an equilateral triangle with equal sides if these forces combine to make it.

Hence, the correct option is (B).