A hydrometer is an instrument used to determine liquid density. A simple one is

Question

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 let the atmosphere lift a sample of the liquid of interest into a tube containing a calibrated rod of known density. 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 p=p0L)/(L-H)

Explanation / Answer

When the rod floats, the weight of the displaced fluid equals the weight of the rod. density of fluid* g* V (displaced) = average density * g * V(rod) But, assuming a cylindrical rod V= (pi) *(r^2)*L The volume of fluid displaced is the same as the volume of the rod that is submerged, V (displaced) =(pi) *(r^2)*(L-h) thus density reduces to (average density)*(L/(L-h)) p=p0(L)/(L-h) Please let me know if u have doubts ... thank you

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