Surface tension is originated as a result intermolecular forces. Surface tension is concerned with only liquid.
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Why ends/edges of glass become round on heating?
Molten gas tries to acquire the minimum surface area and hence heats up due to surface tension. Rounding off the edges makes them acquire the minimum surface area.
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Why does the oil spread over the water?
Surface tension of oil is less than water, therefore, oil spreads over water and do not mix with each other.
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Does the surface tension of a liquid depend on the area of the free surface of liquid?
Surface tension of the liquid is independent of the area of the free surface of liquid.