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Variable Density Rotational Inertia

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The mass density of a solid cylinder of radius R and height h is a function of the radial distance r from its central axis, given by ρ(r)=ρ0rR\rho(r) = \rho_0 \frac{r}{R}, where ρ0\rho_0 is a constant. Which of the following gives the rotational inertia of the cylinder about its central axis in terms of its total mass M?

A

(2/3)MR²

B

(1/2)MR²

C

(3/5)MR²

D

(4/7)MR²

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