A chain of length L is placed on a horizontal surface as shown in figure. At any instant X is the length of chain on rough surface and the remaining portion lies on smooth surface. Initially X = 0. A horizontal force P is applied to the chain (as shown in figure). In the duration X changes from X = 0 to X = L for chain to move with constant speed –

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For chain to move with constant speed P needs to be equal to frictional force on the chain as the length of chain on the rough surface increases. Hence the friction force f K = µ K N increases.
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