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**1. Homework Statement**

There is a gaseous spherical planet with a nonconstant density rho(r) = rho_o (1 - r / R), where rho_0 is the maximum density attained at the planet's core, R is the radius of the planet, and r is the distance from the center of the planet.

Use calculus to find the total mass of the planet in terms of rho_0 and R. Then find the moment of inertia of the planet in terms of its total mass M and R.

**2. Homework Equations**

**3. The Attempt at a Solution**

I found the Mass of the planet as (rho_o * pi *R

^{3})/3

I integrated thin spherical shells to find the total mass using the integral - 4piR

^{2}dr*density

Then I found average density as rho_o/4

Now, I am using the integration of thin solid disks to find teh moment of inertia of the sphere...which comes out to be 8/15 * density*pi R

^{5}

If we substitute the averahe density in terms of M in the above equation, the answer comes out to be 2/5 * M*

^{R2}but I think the correct answer is 4/15*M*R

^{2}

Can anyone tell me if I am correct or am I doing something wrong