# Centre of mass of a rod with varying density

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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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Step by step explanations to this tricky problem. A center of mass of a rod with varying densities are determined.

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Let us take the cross sectional area of the rod as α. Now we will determine the mass of a small element of length dx distant x from the left end.

It is given that the density varies as A+Bx , thus the mass of this small element would be (A+Bx) α dx (density X vol gives the mass, ...

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