What is the ratio between the depths they will sink into the ice?

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The discussion centers on the thermal dynamics of two copper vessels, one weighing 20g and the other 50g, both heated to 85 degrees Celsius, placed on ice. The key conclusion is that the depth to which each vessel sinks into the ice is influenced by their mass and the area of contact with the ice. The larger mass (50g) vessel will take longer to cool to 0 degrees Celsius due to its greater thermal energy content, adhering to the principles of conservation of energy.

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q.if two copper vessels of mass 20g and 50g are heated to 85 degrees celsius and are put onto similar ice blocks, what is the ratio between the depths they will sink into the ice?
 
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Some more information would be rather helpful here. For instance, I would think the area where ice and copper touch are probably different: different weight+same material -> different size.
 
Assuming that the bases of the copper vessels were the same size, consider: which of these vessels would take longer to cool to 0 degrees (the assumed temperature of the ice)?

THen answer the following question: "why"? (Using conservation of energy as your guide).
 

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