Two cubes A and B of same shape, size and mass are placed on...

Two cubes $A$ and $B$ of same shape, size and mass are placed on a rough surface in the same manner. Equal forces are applied on both the cubes. But at the cube $A$, the force is applied at the top in horizontal direction. But at the cube $B$ just above the centre of mass of the cube in the same manner. Then: (a) $A$ will topple first (b) $B$ will topple first (c) both wili topple at the same time (d) none of the above

Two cubes $A$ and $B$ of same shape, size and mass are placed on a rough surface in the same manner. Equal forces are applied on both the cubes. But at the cube $A$, the force is applied at the top in horizontal direction. But at the cube $B$ just above the centre of mass of the cube in the same manner. Then:
(a) $A$ will topple first
(b) $B$ will topple first
(c) both wili topple at the same time
(d) none of the above

Key Concepts

Torque

Torque is the rotational analog of force, defined as the product of a force and its perpendicular distance from a pivot point. When a force is applied at a point away from the center of mass, it creates a moment that tends to rotate the object about its base. In problems involving toppling, a higher torque can induce rotation more readily, overcoming the restoring torque due to gravity at the object’s center of mass.

Center of Mass

The center of mass is the point at which the mass of the object can be considered to be concentrated. Forces acting through the center of mass cause translational motion without generating rotational effects. Conversely, forces applied away from the center of mass create a torque. In stability analyses, the location of the center of mass is crucial because it determines the object's ability to resist tipping when subjected to external forces.

Force Application Point

The point at which a force is applied determines the magnitude of the resulting torque. A force applied further from the center of mass, such as at the top of an object, generates a larger moment arm and thus a larger torque compared to an equal force applied near the center. This concept is central to understanding why an object subjected to a higher torque is more prone to toppling.

Toppling

Toppling refers to the loss of balance of an object, usually when the applied torque exceeds the stabilizing torque due to gravity. When external forces produce a moment that shifts the net force outside the base of support, the object will begin to rotate and eventually tip over. This concept is extensively analyzed in statics and dynamics to assess the stability of structures or objects under various forces.

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