A hydrometer is an instrument used to determine liquid density. A simple one is sketched in the figure below. The bulb of a syringe is squeezed and released to lift a sample of the liquid of interest into a tube containing a calibrated rod of known density. (Assume the rod is cylindrical.) The rod, of length L and average density 0, floats partially immersed in the liquid of density . A length h of the rod protrudes above the surface of the liquid. Show that the density of the liquid is given by
=
0L
L − h
.
(Do this on paper. Your instructor may ask you to turn in this work.)

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laobaba38 laobaba38 · Answer 1 · 2021-06-19T15:26:30+02:00

Answer:

weight of rod =weight of liquid displaced

mass of the rod ×g =mass of liquid displaced ×g

(g cancelled out)

mass of the rod =mass of liquid displaced

density of rod ×volume of rod =density of liqiud ×volume of liquid displaced

O×cross section area of rod ×height of rod =density of liquid ×Cross section area of rod ×height of rod under the surface

O×L=density of liquid ×(L-h)

then density of liquid =OL/(L-h) shown as required

sp10925 sp10925 · Answer 2 · 2022-06-07T14:08:05+02:00

The density of the liquid is given by =OL/L − h

Density is the ratio of mass of an object and its volume.

According to the Archimedes principle, weight of rod = weight of liquid displaced

mass of the rod ×g =mass of liquid displaced ×g

So, mass of the rod =mass of liquid displaced

Mass in terms of density is substituted,

density of rod × volume of rod =density of liquid ×volume of liquid displaced

O× cross section area of rod ×height of rod =density of liquid ×Cross section area of rod ×height of rod under the surface

O×L=density of liquid ×(L-h)

Then, density of liquid =OL/(L-h).

Learn more about density.

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