We can also define centre of mass in terms of vector. let rᵢ be the position vector of the ith particle and R be the position vector of the centre of mass, then

#### Centre Of Mass Of Rigid Continuous Bodies

For a real body which is a continuous distribution of matter, point masses are then differential mass elements dm and centre of mass is defined as

If origin is the co-ordinate of centre of mass, then

∫x dm = ∫y dm =∫z dm = 0

#### Centre Of Mass Of A Uniform Thin Road

We consider a uniform thin rod AB of mass M and length L. The rod is held along x-axis with its end A at the origin whose co-ordinate is (0,0). Let the element is placed side by side of length dx at distance x from the origin, then

Thus, it means that the centre of mass of thin rod AB lies at point (L/2,0) i.e Centre between its end A and B.

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