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1. Homework Statement

1. Homework Statement

Consider an annulus with inner radius R

_{1}and outer radius R

_{2}. The mass density of the annulus is given by σ(r)=C/r, where C is a constant. Calculate the total mass of the annulus.

## Homework Equations

σ(r)=C/r

dm=σ(r)dA, assuming we can split the annulus into small shells with area dA.

dA= 2πrdr, where r is the radius from the centre of the annulus to the shell, and dr is the thickness of each shell

## The Attempt at a Solution

If we split the annulus into small shells, like I said above, and sum up their masses through an integral, we should get the total mass (assuming that R

_{2}and R

_{1}are the upper and lower limits of integration respectively):

So, we get m=∫2πr(C/r)dr after combining the equations above, simplifying gives m=2πC∫dr

Integrating with the limits gives m=2πC(R

_{2}-R

_{1}).

Is this logic correct? Thanks heaps guys!