A uniform rope of linear mass density \( \lambda \) and length \( l \) is coiled on a smooth hor...

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A uniform rope of linear mass density \( \lambda \) and length \( l \) is coiled on a smooth horizontal surface as shown in the figure. One end is pulled up with constant velocity \( v \). Then, the average power applied by the external agent in pulling the entire rope just off the ground is
(A) \( \frac{1}{2} \lambda l v^{2}+\frac{\lambda l^{2} g}{2} \)
(B) \( \lambda g v \)
(C) \( \frac{1}{2} \lambda v^{3}+\frac{\lambda \lg v}{2} \)
(D) \( \lambda g v+\frac{1}{2} \lambda v^{3} \)
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