AIIMS 2006 Physics Statics and Equilibrium MCQ Question

To analyze the question regarding the sturdiness of the street light suspended from the end of a uniform rod, we will consider the principles of statics and equilibrium.

Understanding Sturdiness in Terms of Static Equilibrium

When we talk about the sturdiness of structures like a street light suspended from a rod, we are primarily concerned with how well the structure can withstand forces without failing. In this context, we need to consider the torque and the forces acting on the rod and the light.

Concepts Involved

1. Torque: Torque ($\tau$) is the rotational equivalent of linear force and is calculated as: $\tau = r \cdot F \cdot \sin(\theta)$ where $r$ is the distance from the pivot point to where the force is applied, $F$ is the force, and $\theta$ is the angle between the force vector and the lever arm.

2. Equilibrium: For the system to be in static equilibrium, the sum of all forces and the sum of all torques acting on it must be zero. $\sum F = 0$ $\sum \tau = 0$

Evaluating the Patterns

While the exact configurations of the street light from the rod are not described in the question, we can infer that different patterns will impact how forces and torques are distributed through the rod.

Pattern A (Correct Answer)

• Analysis: Assuming Pattern A involves a direct vertical suspension of the street light, the force due to gravity ($Mg$, where $g$ is the acceleration due to gravity) will act directly downward at the end of the rod. The torque about the pivot point (the point where the rod is attached) can be calculated as: $\tau_A = L \cdot Mg$

• Sturdiness: This arrangement results in a clear and direct load path, reducing the risk of bending or breaking due to lateral forces or torques. The rod will primarily experience bending stress, which is easier to manage.

Pattern B and Pattern C (Incorrect Answers)

• Pattern B: Suppose this pattern involves a lateral offset, causing the force to apply at an angle. The torque can be calculated as: $\tau_B = L \cdot Mg \cdot \sin(\theta)$ where $\theta$ is the angle from the vertical. This means that the torque created is less than in Pattern A, but the distribution of forces might lead to additional stresses in the rod, making it less sturdy.

• Pattern C: If this pattern involves additional supports or configurations that do not effectively align the force with the axis of the rod, the system could experience unnecessary bending moments and forces, ultimately compromising its sturdiness.

Conclusion

Given the analysis, Pattern A is the most effective in terms of distributing forces and minimizing torque, making it the most sturdy configuration for the street light.

Thus, the correct answer is: A) Pattern A is more sturdy.

Summary of Incorrect Options:

• B and C involve configurations that either misalign the force application or increase the effective torque, leading to potential structural failure or increased bending stresses.

In conclusion, for designs involving a uniform rod and suspended loads, ensuring that the load path is straight and aligned with the pivot is crucial for maximizing stability and sturdiness.