A hydrometer is a device used to measure the density of aliquid. It is a cylindr

Question

A hydrometer is a device used to measure the density of aliquid. It is a cylindrical tube weighted at one end, so that itfloats with the heavier end downward. The tube is contained insidea large "medicine dropper," into which the liquid is drawn usingthe squeeze bulb (see the drawing). For use with your car, marksare put on the tube so that the level at which it floats indicateswhether the liquid is battery acid (more dense) or antifreeze (lessdense). The hydrometer has a weight of W = 6.39× 10-2 N and a cross-sectional area ofA = 7.07 × 10-5m2. How far from the bottom of the tube shouldthe mark be put that denotes (a) battery acid( = 1280 kg/m3) and(b) antifreeze ( = 1073kg/m3)?

Explanation / Answer

    as the magnitude of the buoyant forceFB equals the weight W of the tube we have     FB = W     the mass is the density of the fluid times thedisplaced volume     m = V     the result is that the weight of the displacedfluid is V g     so FB = W becomes     V g = W     if h is the height beneath the fluid surfacethen     V = A h     A h V g = W (a)     hacid = W / acid Ag            = ............ m (b)      hatifreeze = W /antifreeze A g            = ............ m

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