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That would depend upon the density of the oil (which will depend upon temperature), how absorbant of oil the substance was and how deep the oil is.

Assuming the substance does not absorb any of the oil then depending upon the oil various things would happen:

In some oils such as Car oils, Coconut oil, Crude oil California, Linseed oil which all have a density less than 0.95 g/ml the substance would sink (unless the oil was not deep enough in which case the substance would sit on the bottom of the container and appear above the surface of the oil).

In other oils such as Castor oil, Crude oil Mexican, Rosin oil which all have a density greater than 0.95g/ml the substance would float.

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Q: What would happen if a substance with a density of 0.95gml was placed in oil?
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