# Mass of an annulus with variable mass density

• Royalsamplerz

#### Royalsamplerz

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

1. Homework Statement

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.

## 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 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!

Yes, that is correct.