# Homework Help: Mass of an annulus with variable mass density

1. Jun 12, 2016

### Royalsamplerz

Hey guys, I just wanted to check if my method for solving this problem is correct.

1. The problem statement, all variables and given/known data

Consider an annulus with inner radius R1 and outer radius R2. 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.

2. Relevant 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

3. 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 R2 and R1 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(R2-R1).

Is this logic correct? Thanks heaps guys!

2. Jun 12, 2016

### PeroK

Yes, that is correct.