APFIVE Variable Density Rotational Inertia
A solid cylinder of radius R and height h has a mass density that varies with radial distance r from the central axis as $$\rho(r) = \rho_0 \frac{r}{R}$$, where $$\rho_0$$ is a constant. What is the rotational inertia about its central axis in terms of its total mass M?
A
(4/7)MR²
B
(1/2)MR²
C
(2/3)MR²
D
(3/5)MR²
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