Consider two uniform solid spheres where both have the same diameter, but one has twice the mass of the other. how much larger is the moment of inertia of the larger sphere compared to that of the smaller sphere?

The moment of inertia of the large sphere will be twice that of the smaller sphere.
   The formula for the moment of inertia for a solid sphere is:
 I = (2/5)mr^2
 where
 I = moment of inertia
 m = mass
  r = radius

   Since both spheres have the same diameter, they also have the same radius, so the only change is their mass. And the moment of inertia is directly proportional to their mass as shown by the above formula. So the sphere with twice the mass will have twice the moment of inertia, or 2 times.