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I attempted a question that involves a cube of sides 8 cm suspended in a container of oil and water with oil floating above water. The entire cube is basically fully suspended and floating with 5cm height in oil and 3 cm height in water. Density of water=1000kg/m3 and density of oil=800kg/m3. I calculated the density for the same cube in oil is 500kg/m3 and then the density of cube in water is 375kg/m3, which adds up to a density of 875kg/m3 for the cube. This led me to realise that the same cube has different densities in fluids with different densities? I’ve always thought density is somewhat constant but now why is this so?

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First note that since oil and water have different densities, they will exert different buoyant forces on the cube, since this force is given by $$F_b=\rho Vg$$ where $V$ is volume and $g$ is the strength of the gravitational field. Note the dependance on the density $\rho$.

Remember that density $$\rho=\frac mV$$

If an object retains its mass $m$ and volume, then it's density will remain the same.

So density is an intrinsic property and does not change depending upon where the object is or upon the composition of its surroundings.

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Your mistake is trying to calculate two separate densities and then add them together. The correct approach is

  1. Calculate the mass of water displace day by the cube.
  2. Calculate the mass of oil displaced by the cube.
  3. Add the two masses together - this gives you the total mass of the cube (unlike densities, masses can be added together).
  4. Divide the mass of the cube by its volume to find its average density.
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  • $\begingroup$ I calculated the densities separately as it seemed logical to apply law of flotation that way but I’ll try out your method which is probably correct. Thanks guys, for your help! $\endgroup$
    – Kay
    Jun 22 at 23:19

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