The centre of gravity of a system of rigid bodies coincides with their

The centre of gravity of a system of rigid bodies coincides with their centre of mass if and only if

their centre of mass is at their geometrical centre

the acceleration due to gravity is same throughout the system of bodies

the rigid bodies have same uniform mass densities

the rigid bodies are very large

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UPSC Geoscientist – 2022

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The centre of mass (CM) of a system is determined solely by the distribution of mass. The centre of gravity (CG) is the point where the net gravitational force acts on the system. The CG and CM coincide if and only if the gravitational acceleration (g) is uniform throughout the system. If g is constant, the weight of each part of the system is directly proportional to its mass (wᵢ = mᵢg), and the formula for the CG position becomes identical to that for the CM position. If g varies significantly across the system (e.g., a very large object or a system in a non-uniform gravitational field), the CG and CM will not coincide.

– CG and CM coincide when gravitational acceleration (g) is constant across the system.
– CM depends on mass distribution.
– CG depends on both mass distribution and the distribution of the gravitational field.

For most objects on Earth, the variation in g over the object’s size is negligible, so CG and CM are effectively at the same location. However, in theoretical physics or for extremely large systems (like a mountain), the slight variation in gravity could cause a separation between the two points.

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