While you are watching a TV show about life in the ancient world, you see that the people in one village used a solid sphere made out of clay as a kind of pulley to help hault up water from well. A well-greased wooden axle was placed through the center of the sphere and fixed in a horizontal orienation above the well, allowing the sphere to rotate freely. To demonstrate the depth of the well, the host of the program completely wrapped the rope around the sphere and suspended the bucket from one end. She then released the bucket, from rest and allowed it to descend to the botton of the well unwinding the string from the sphere as it went. It took 2 seconds. You wonder what the depth of the well was so you decide to calculate it. You estimate that the sphere has twice the mass of the bucket and assume that the mass of the rope can be neglected. You look up the moment of inertia of a sphere about an axis through its center of mass and find it as 2/5mr2.