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When we take two containers and fill them both with same or different liquids and put one in the other and let the container reach equilibrium, why do we observe that both the liquid levels match, supposing the containers are ideal and are massless? (Diagram for reference)

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    $\begingroup$ In general, the two levels will not match. It depends on how much water is in there, and what the weight of the container is. If you pour a bit of water in a boat, the boat will not suddenly rise to equalise the water levels inside and outside the boat. $\endgroup$
    – fishinear
    Jan 23, 2022 at 11:31
  • $\begingroup$ @fishinear I think you can post this as an answer. $\endgroup$
    – Bernhard
    Jan 23, 2022 at 14:53
  • $\begingroup$ @fishinear What if the containers were massless, do you still think that the levels wouldn't match? $\endgroup$ Jan 23, 2022 at 15:11

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If the liquids have the same density and the inner container is massless the levels will match. Otherwise, they won't (except in some special cases).

In general, you just need to use Archimedes's law: $V_{\mathrm{displaced}} \rho_{\mathrm{outside}} g = M g$, where $M$ is the total mass of the inner vessel and liquid contained in it.

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