Question

Which of the following statements are true for Lami's Theorem
(A). It deals with equilibrium of forces.
(B). There should be three forces acting at a point.
(C). The forces should be coplanar.
(D). The angle between forces should be \(120^\circ\).
Choose the correct answer from the options given below:

• A. (A), (B) and (C) only.
• B. (B), (C) and (D) only.
• C. (C), (D) and (A) only.
• D. (A), (B) and (D) only.

Hint:

Lami's Theorem is a restatement of the Sine Rule from trigonometry applied to a closed triangle of forces in static equilibrium. It is highly useful for solving concurrent three-force problems quickly.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Lami's Theorem is a useful principle in statics. It simplifies the analysis of a system of concurrent, coplanar forces in static equilibrium without needing to resolve the forces into horizontal and vertical components.
Key Formula or Approach:
For three concurrent, coplanar forces \(A\), \(B\), and \(C\) in equilibrium: \[ \frac{A}{\sin\alpha} = \frac{B}{\sin\beta} = \frac{C}{\sin\gamma} \] where \(\alpha\), \(\beta\), and \(\gamma\) are the angles opposite to the forces \(A\), \(B\), and \(C\), respectively.

Step 2: Detailed Explanation:
Let us evaluate each statement:

Statement (A): Lami's Theorem is derived specifically for a body in static equilibrium under a force system. Thus, Statement (A) istrue.

Statement (B): The theorem applies strictly to a system of exactly three concurrent forces (forces that meet at a single point). Thus, Statement (B) istrue.

Statement (C): The three forces must lie in the same two-dimensional plane (coplanar) for the trigonometric sine relationship to hold. Thus, Statement (C) istrue.

Statement (D): There is no requirement for the angles between the forces to be equal to \(120^\circ\). The angles can be any values, as long as their sum is \(360^\circ\) and no single angle is \(180^\circ\) (which would align the forces). Thus, Statement (D) isfalse.
Combining these, only statements (A), (B), and (C) are true.

Step 3: Final Answer:
The true statements are (A), (B), and (C), which corresponds to Option (A).