Question

One end of an iron chain is fixed to a sphere of mass M = 10 kg and of diameter D = 0.3 m (the volume of such a sphere is V = 0.0141 m³), while the other end is free. The length l of the chain is 3 m and its mass m is 9 kg. The sphere with the chain is in a reservoir whose depth H = 3 m.

Determine the depth at which the sphere will float, assuming that iron is 7.85 times heavier than water.

Answer 1

Obviously, in equilibrium, the sphere is at a certain height h above the bottom of the reservoir, and some part of the chain lies at the bottom, while the other part hangs vertically between the bottom and the sphere (Fig. 193).

By hypothesis, we can state that the sphere is completely submerged in water (otherwise, nearly the whole chain would hang, which is impossible in view of the large density of iron). Then the height h can be obtained from the equality, of the total force of gravity of the sphere and the hanging part of the chain and the buoyant force acting on them:

The depth at which the sphere floats is H - h = 1.4 m.