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Would an object that weighed 21.00 g sink in a density of 13.6 g mL?

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That depends on the density of the object along with bouyancy. A 2g rock will sink in water whereas a 2000 kg boat will not (if made right). It doesnt matter what something weighs. An object floats because it displaces an amount of water equal to or more than its own weight. A boat that weighs 2000 kg will float becuase its shape displaces enough water. The 2 kg rock's shape does not displace enough water, and it sinks.

For your question, either the object needs to be really big/wide (to displace the liquid) or be less dense than the liquid. From the info you gave, we can't answer your question.

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