A regular polygon of n sides is placed on a rough surfac...

A regular polygon of $n$ sides is placed on a rough surfac vertically as such one of the side of regular polygor touches the surface. A force is applied horizontally at th top. The chosen value of $n$ are 3,5 and 8 . For which valu of $n$, the polygon first is likely to topple? (a) 3 (b) 5 (c) 8 (d) all the above

Key Concepts

Rotational Equilibrium

This concept refers to the state where the sum of all torques (moments) acting on a body is zero, meaning there is no net angular acceleration. It is key to determining when an applied horizontal force creates enough moment about a pivot to overcome the stabilizing torque from the weight of the body, leading to toppling.

Center of Mass

The center of mass is the point at which the mass of an object is concentrated for the purpose of analysis in dynamics. Its location relative to the base of support is crucial for stability because if the vertical line through the center of mass falls outside the support area, the body will begin to tip.

Moment Arm

A moment arm is the perpendicular distance from the pivot point to the line of action of a force. It plays an essential role in rotational dynamics, as the torque produced by a force is equal to the product of the force magnitude and its moment arm, determining the potential for rotation or toppling.

Regular Polygon Geometry

The study of regular polygon geometry, including concepts like the apothem, circumradius, and the angular distribution of vertices, is important for analyzing stability. These geometric parameters determine both the height at which a force is applied and the distance between the center of mass and the pivot point, thereby influencing the conditions required for toppling.

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