Re: what happens when a solid and liquid of same densities are place in a jar

If two objects have the same density then for a given mass, they occupy the same volume. For example, if their densities are 1.62 g/cm3, then a 1 cubic centimeter volume of each will weigh exactly 1.62 grams.

The consequence for this, in terms of floating or immersion of the solid in the liquid, is that they will have "neutral bouyancy" with regard to one another.

If you put the cube into the liquid, it will stay where you put it (provided that there are no other forces at play). That is, if you put the solid at the bottom of a container holding liquid of the same density, then it will stay at the bottom. If halfway, then it will stay halfway. If at the top, then it will stay at the top. All of the forces on the solid are balanced and there is no net force to cause it to move.

More to the point, it will not be "floating half-submerged" in the liquid but be floating completely submerged or even with the surface. Bouyancy relies on a differential in the density of the two components and without a difference, they will simply displace one another. There is no additional force to get the solid out of the liquid so that it is "half- submerged".

This is the principle that is used in submarines. By alterring the amount of water or air in their ballast tanks, they can match the density of the water and they then sit at exactly that depth (or density). Neutral bouyancy means that they do not rise or sink but travel at the same level.

With regard to two liquids, there are a couple of other questions that would need to be answered. The first is - are they miscible? That is, can they mix in any proportion and never separate? If the answer is "Yes", then the two liquids would, indeed, do just that. They would mix thoroughly be a process of random diffusion.

But if they are not miscible, then that leads to the other question - are you pouring them carefully to create a layered effect or just sloshing them together? If they are poured carefully, then one of the liquids will stay on top and the other on the bottom because they don't mix. They will stay relatively separate even though they have the same density because of the miscibility of the two liquids.

If two liquids are sloshed together and are not miscible, then the two liquids will form mutual globs or blobs in one another. Think of a lava lamp but without the currents or heat flow. A neat effect but hard to do.

Hope this answers your questions.