(12 points) In this question, we will compare the masses, mg and mE, and moments of inertia, Ig and Ig, of both a solid sphere B = {r? + y + 22 < 1} and a solid truncated sphere (that is, sliced to remove a spherical cap) E = {r + y? + 2? < 1}n {x < } of uniform densities, pg and pE, that are precessing about the r-axis. (a) (5 points) Show that the masses of the unit and truncated spheres are mg = s0T and mg = (b) (5 points) The moment of inertia Iy of an object V rotating about the r-axis is Iy = ( + 2*)p(x, y, z) dV. Using cylindrical coordinates, compute the moments of inertia Ig and Ig of the unit sphere and the truncated sphere. (e) (2 points) If unit sphere B and truncated sphere E have the same mass M, but different uniform densities, then which object will have the larger moment of inertia? Which will roll down an inclined plane fastest?