A common hydromenter with astem of 10cm long and volume one-tenth of whole hydrometer, floats with 2cm of stem above the water surface. What is the density of the liquid in which the hydrometer floats with 4cm abave the surface?

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For water the total length submerged is `L_1=10-2 =8cm`. For the second liquid, the total length submerged is `L_2 =10-4 =6 cm` .

The hydrometer works on Archimedes principle, so that the buoyant force is equal to the weight of the liquid corresponding to the volume submerged.

Since the mass of the hydrometer is the same in both cases, the buoyant force needs to be the same:

`rho_1*L_1*S =rho_2*L_2*S`

Here above `L*S` is the volume of the hydrometer that is submerged in liquid. Therefore

`rho_2 =rho_1*L_1/L_2 =1000*8/6 =1333 (kg)/m^3`

Answer: The density of the second liquid is `rho = 1333 (kg)/m^3`

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