A chain of length \( L \) is placed on a horizontal plane as shown in figure. At any instant \( ...

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A chain of length \( L \) is placed on a horizontal plane 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 direction \( x \) changes from \( x=0 \) to \( x=L \), for chain to move with constant speed.
(a) The magnitude of \( P \) should increase with time
(b) The magnitude of \( P \) should decrease with time
(c) The magnitude of \( P \) should increase first and then decrease with time
(d) The magnitude of \( P \) should decrease first and then increase with time
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