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The frictional force between solids operates even when they do not move with respect to each other.

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The frictional force between solids operates even when they do not move with respect to each other. Do we have a viscous force acting between two layers even if there is no relative motion? 

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No. Though both frictional force and the viscous force oppose the relative motions, it is the difference between them that viscous force only comes into play when there is a relative motion between two layers.

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