Oily Sphere
A vessel contains oil of relative density" 0.8" floating over mercury with a relative density of . A sphere floats with half of its volume in oil and with its other half in mercury.
If the density of the sphere is , in it's simplest form, then find . ( A/B is in the CGS Unit of density )
The answer is 41.
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1 solution
In the problem , it's given that oil has a relative density of 0.8 .
=> Density of oil = (0.8 1)g/cc = 0.8 g/cc
Similarly , Density of mercury = (68/5 1)g/cc = 68/5 g /cc = 13.6 g/cc
Now , according to the method of mixtures , we know that if two liquids of densities "d1" and "d2" occupying the same volume are mixed , then the density of the mixture is d1+d2/2.
Substituting the densities we got , we get
Density of the sphere (mixture in this case) = (0.8+13.6)g/cc / 2 = 14.4/2 g/cc = 36/5 g/cc
=>A/B = 36/5
=> A+B= 36+5 = 41