Mass of an annulus with variable mass density

[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!

 

[PeroK]

Yes, that is correct.