The cork floats because its density is less than the density of water, resulting in an upthrust that is greater than its weight, whereas the nail sinks due to its higher density.
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The cork floats in water because its density is less than that of water, allowing the buoyant force exerted by water to exceed its weight, keeping it afloat. The nail sinks because its density is greater than that of water, causing it to be denser and thus sink.