Question

why warm air is lighter than cold air give reason.

Answer 1

Warm air molecules contain more heat energy, which causes them to move more rapidly. Rapid movements lead to more frequent collisions between molecules which causes the molecules to separate. Therefore there is more empty space between molecules in warmer air and the air is lighter.

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Answer 2

Hot air rises because when you heat air (or any other gas for that matter), it expands. When the air expands, it becomes less dense than the air around it. The less dense hot air then floats in the more dense cold air much like wood floats on water because wood is less dense than water.