While you are watching a tv show about life in the ancient world, you see that t

Question

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 haul up water from a well. A well-greased wooden axle was placed through the center of the sphere and fixed in a horizontal orientation 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 bottom 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 is neglected. moment of inertia for sphere is 2/5mr^2.

I got 9.81 m for the depth of well but I don't think that's correct.

Explanation / Answer

I think it is a case of free fall.Mass of bucket and mass of rope and inertia etc. quantities are not useful to found depth of well

H =ut +1/2gt2

as t=2 and u =0

H = 9.8*2*2/2 = 19.6m

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