A uniform cylindrical hydrometer of mass 20g and cross sectional area 0.54cm2 floats upright in a liquid. If 25cm of its length is submerged, calculate the relative density of the liquid. (Density of water = 1 gcm-3)
1.54
1.48
1.25
0.80
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Answer: 1.48
Relative density= density of liquid ÷ density of water
density of water=1gcm^-3
density of liquid
=mass/volume
=mass/Area*height
=20 / (0.54*25)
=20/13.5
=1.48gcm^-3
Therefore;
Relative density
=1.48gcm^-3/1gcm^-3
=1.48 ( Note Relative Density has no unit)
Mh = 20g
CSA= 0.54cm3
h of hygrometer in H²O = 25cm
Dw = 1g/cm3
Df = ?
Dr = ?
but Dr = Df/Dw
Df = Mf/Vf
but according to Archimedes principle, a floating body displaces its own mass of fluid.
=> Mf = Mh=20g
and also, according to the law of flotation, a floating body displaces its own volume of fluid.
vf = Vh
Vh = CSA × h
Vh = 0.54× 25 =13.5cm3
Vf = Vh = 13.5cm3
Df = Mf/Vf
=> Df = 20g/13.5cm3 = 1.48g/cm3
Dr = Df/Dw
Dr = (1.48g/cm3)/(1.00g/cm3)
Dr = 1.48
Note that it has no unit because it is a ratio of two similar quantities.
[D = density
r, f, w, h = relative, fluid, water and heigt respectively
V = volume
]
A uniform cylindrical hydrometer of mass 20g and cross sectional area 0.54cm2 floats upright in a liquid. If 25cm of its length is submerged, calculate the relative density of the liquid. (Density of water = 1 gcm-3)
