Answer
a) $M=\frac{2\pi\rho_0wR^2}{3}$
b) $I=\frac{3MR^2}{5}$
Work Step by Step
a) We know that the mass is equal to the integral of the quantity of the density times the volume. Thus, we find:
$M = 2\int_0^R \frac{\rho_0r}{R}\pi r^2 w dr $
$M=\frac{2\pi\rho_0wR^2}{3}$
b) Using the definition of moment of inertia, we find:
$I=\frac{3MR^2}{5}$
