Moment of inertia with varying density

[PhilosophyofPhysics]

I had to find the moment of inertia of a sphere of varying density where the density is some constant times the radius.

I used the equations from here

http://hyperphysics.phy-astr.gsu.edu/hbase/isph.html

I inserted this d=cr in for the density.

For the mass I used dm=4(pi)(d)r^2dr, inserted the density, integrated and solved for c.

After substitution I the answer I got was 2/15mr^2.

Does this sound right?

 

[Mentz114]

The answer should be between the solid sphere value and the thin shell value, so your answer is too small. I did a rough calculation and got 1/2Mr^2.

Can you show more of your working ?

 

[mjsd]

your dm element seems ok if you are taking thin shell as your differential element. I got $$\frac{4}{9} MR^2$$. you should check whether you have got constant c correct.