Since the balls have equal diameter and equal mass, their volume and density are also equal. However, the mass distribution is not equal, so they will have different moments of inertia - the hollow sphere has its mass concentrated at the outer edge, so its moment of inertia will be greater than the solid sphere. Applying a known torque and observing which sphere has the largest angular acceleration will determine which is which. An easy way to do this is to "race" the spheres down an inclined plane with enough friction to prevent the spheres from sliding.

Then, by conservation of energy

mgh = 1/2 mv^2 + 1/2 Iw^2

Since the spheres are rolling without sliding, there is a relationship

between velocity and angular velocity

w = v / r


mgh = 1/2 mv^2 + 1/2 I (v^2 / r^2) = 1/2 (m + I/r^2) v^2


v^2 = 2mgh / (m + I / r^2)

From this we can see that the sphere with larger moment of inertia (I) will have a smaller velocity when rolled from the same height, if mass and radius are equal with the other sphere. Thus the solid sphere will roll faster.

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