Question

Lami's theorem is applicable to

• A. Two concurrent forces
• B. Three non-coplanar forces
• C. Three concurrent forces in equilibrium
• D. Any number of forces

Hint:

Lami's theorem is used only when three concurrent forces keep a body in equilibrium.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Lami's theorem is a principle in statics that relates the magnitudes of three forces acting on an object to the angles between them. The question asks for the specific conditions under which this theorem can be applied.
Step 2: Key Formula or Approach:
Lami's Theorem states: {"If three coplanar, concurrent forces acting on a body keep it in equilibrium, then each force is proportional to the sine of the angle between the other two forces."} Mathematically, if F$_1$, F$_2$, and F$_3$ are the forces, and $\alpha$, $\beta$, and $\gamma$ are the angles opposite to them respectively (i.e., $\alpha$ is the angle between F$_2$ and F$_3$), then: \[ \frac{F_1}{\sin \alpha} = \frac{F_2}{\sin \beta} = \frac{F_3}{\sin \gamma} \] Step 3: Detailed Explanation of Conditions:
For Lami's theorem to be applicable, the following conditions must be met: 1. Three forces: The theorem applies only to a system of exactly three forces. 2. Concurrent: The lines of action of all three forces must intersect at a single point. 3. Coplanar: All three forces must lie in the same plane. (This is usually implied but is a necessary condition). 4. In equilibrium: The net effect of the three forces must be zero; i.e., the body is not accelerating. Let's evaluate the options based on these conditions: - (A) Two concurrent forces: Incorrect, it must be three forces. - (B) Three non-coplanar forces: Incorrect, the forces must be coplanar. - (C) Three concurrent forces in equilibrium: Correct, this statement includes all the key conditions. - (D) Any number of forces: Incorrect, it applies only to three forces. Step 4: Final Answer:
Lami's theorem is applicable to a system of three concurrent, coplanar forces that are in equilibrium. Therefore, option (C) is the correct answer.