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Why does a body topple over only when the perpendicular from its centre of gravity does not pass through its base?

I had read a paragraph on it from a book by Y. Perelman. I did find a half-satisfying answer to this question but I wanted to get a description and a mathematical view, if possible

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Why does a body topple over only when the perpendicular from its centre of gravity does not pass through its base

One of the requirements for static equilibrium is that the sum of the moments about any point has to equal zero, otherwise there will be rotation. When the perpendicular from the center of gravity of an object does not pass through its base, if there are no other external forces there will be a net moment about base due to its weight and the object will topple.

See the diagram below. Given that the only external force acting on the object is its weight, once the perpendicular through the CG goes beyond point A on the base, there will be a net clock wise moment about A and toppling occurs. When the perpendicular just intersects A, the structure is unstable and toppling is imminent.

Hope this helps.

enter image description here

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