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Buoyant Force

The density o...

Question

The density of a substance is 0.6g/cm³. It floats with 2/3^rd of its volume in a liquid. Find the density of the liquid.

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Solution

Let the volume of the substance be V.
So, its weight is = (0.6)(V)(g)
It floats with (2/3)V inside the liquid. So, it displaces (2/3)V volume of liquid.
Weight of the liquid displaced = (d)(2V/3)(g)
[d is the density of the liquid]
Thus, buoyant force = (d)(2V/3)(g)
So, (0.6)(V)(g) = (d)(2V/3)(g)
=> 0.6 = 2d/3
=> d = (0.6)(3)/2 = 0.9 g/cm³
This is the density of the liquid.

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