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When you have an empty cylindrical cup the centre of mass is about halfway up, the same is true with a full cup, but partly full and the combined centre of mass of cup and liquid is below hafway.

I found out that for a prism being filled up lengthwise with liquid, the total centre of mass is lowest when the height of the liquid is the same as the combined centre of mass.

Is this true for any shaped vessel for example a conical cup or a curved cup?

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Yes, this is true in general: As long as the surface is below the combined centre of mass, adding a bit of liquid will add mass below the common centre, hence lower the common centre. Similarly, adding liquid when the common centre is below the surface will add mass above the common centre, hence raise the common centre.

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