Archimedes principle with scales · Physics Brawl 2014 #FoL.8
Physics · fluid-mechanics
Problem
The diagram below shows schematically two situations dealing with an aluminium sphere, cylindrical flask with water and a holding apparatus from which the sphere can be suspended. In the two situations, we have that
a) the holder is placed on top of the scales with the sphere suspended from it. The sphere is fully submerged in the flask which is held off the scales,
b) the same as a), except in this case, the flask rests on the scales.
Find the difference Δm=mb−ma of the readings mb and ma shown by the scales in the situation b) and a) respectively.
The radius of the (homogeneous) sphere is r=1.03 cm, the inner radius of the flask is R=3.01 cm. The height of the water column in the flask with the sphere fully submerged in it is h=5.10 cm. The densities of water and aluminium are ρ=996 kg·m−3 and ρAl=2700 kg·m−3, respectively. The mass of an empty flask is mn=124.5 g. Assume that the suspension part of the holding apparatus is of negligible mass and volume. The rest of the apparatus has a mass of md=523.5 g. The range of values that the scales can measure is sufficient for it to show both readings with accuracy up to 0.1 g. The density of air should be regarded as negligible. State your answer in kilograms.
[Figure: Two diagrams showing situations a) and b) with sphere suspended in water]