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.

© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/physics/classical-mechanics/centre-of-mass-of-a-rod-with-varying-density-1jv

Solution Preview

... 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 ...