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We know that an object floats in a fluid if the density of the object is less than the density of the fluid. When some air or water is heated, it expands. That makes its density less than cooler air or water, so it floats in them.
Warm air rises because warm air has less density than cold air ,warm air also rises because the kinetic energy of the particles is high. Warm water rises or evaporates because evaporation depends on temperature, and the temperature of warm water is sufficient for faster rate of evaporation.
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