Equilibrium of three coplanar forces — Lami’s theorem check: If three coplanar forces acting at a point keep a body in equilibrium, then each force is proportional to the sine of the angle between the other two forces. Is this statement correct?

Introduction / Context:
Lami’s theorem provides a direct relation between the magnitudes of three concurrent, coplanar forces in equilibrium and the angles between them. It is widely used for quick solutions without resolving forces into components.

Given Data / Assumptions:

• Three forces are coplanar and concurrent at a point.
• The body is in equilibrium (net force zero).
• Angles considered are the included angles between the other two forces.

Concept / Approach:
Lami’s theorem states: F1/sin(α) = F2/sin(β) = F3/sin(γ), where α, β, γ are the angles between the other two forces. This follows from constructing the force triangle (closed polygon) and applying the sine rule.

Step-by-Step Solution:
Express equilibrium by a closed vector triangle.Apply the sine rule to the triangle relating side (force) to sine of opposite angle.Conclude proportionality: each force ∝ sine of angle between the other two forces.

Verification / Alternative check:
Resolving forces along two perpendicular axes gives two equations; eliminating one variable leads to the same sine relationships, confirming Lami’s theorem.

Why Other Options Are Wrong:

• Incorrect: would contradict both geometric construction and component-resolution proof.

Common Pitfalls:

• Mistaking the angle at a force tip for an external angle; use the included angle between the other two forces.

Final Answer:
Correct