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Physics

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A hydrometer is an instrument for measuring the specific
gravity of a liquid. For example, producers of maple syrup use the hydrometer to find how much
sugar is in the collected sap. Markings along a stem are calibrated to indicate the specific gravity
for the level at which the hydrometer floats in a liquid. The weighted base ensures that the
hydrometer floats vertically. Suppose the hydrometer has a cylindrical stem of cross-sectional
area 0.400 cm
2.
The total volume of the bulb and stem is 8.8 cm
3
and the mass of the hydrometer
is 4.8 gm.
(a) How far from the top of the cylinder should a mark be placed to indicate a specific gravity of
1.00?
(b) When the hydrometer is placed in some oil, it floats with 7.25 cm of stem above the surface.
What is the specific gravity of the oil?
(c) What is the lowest specific gravity that can be measured with this hydrometer?

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