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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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The magnitude of P should increase with time.

The magnitude of P should decrease with time.

The magnitude of P should increase first and then decrease with time.

The magnitude of P should decrease first and then increase with time.

answer is A.

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Detailed Solution

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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