Question

fluids: A body of density D is dropped from rest from a height h into a lake of density d (d>D). Neglecting all dissipativ forces, the maxm depth to which the body sinks before returning to float on surface is:? (ans: hD/d-D)

Answer 1

# Problem:

A body of density $D$ is dropped from rest from a height $h$ into a lake of density $d$ . Neglecting all dissipative forces, the maximum depth to which the body sinks before returning to float on surface is:?

# Solution:

Assume the volume of body is V. Then according to the law of conservation of energy, we have:

$$D V g (H + h) = d g V H$$

(all the potential energy of the body was used to overcome the buoyancy force $dgV$ ). Thus

$$H = \frac {D h}{d - D}$$

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