# Centre of mass of a rod with varying density

The density of a linear rod of length L varies as ρ = A+Bx where x is the distance from the left end. Locate the centre of mass.

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... dx is the volume).

Since the rod is of length L we need only the X component of the centre of mass.

We know that for a collection of particles, the CM is given by summing the product of particles mass and its coordinate and then dividing the sum by the total mass. Here we have a continuous ...