A perfectly straight portion of a uniform rope has mass M and length L . At end A of the segment, the tension in the rope is T A ; at end B it is T B ( T A ) . The tension in the rope at a dis

Question

A perfectly straight portion of a uniform rope has mass M and length L . At end A of the segment, the tension in the rope is T A ​ ; at end B it is T B ​ ( > T A ​ ) . The tension in the rope at a distance L /5 from end A is

TestHub · Accepted Answer

For the whole rope: T B ​ − T A ​ = M a ...(1) For the piece of length L /5 (mass M /5 ): T − T A ​ = 5 M ​ a ...(2) From (1) and (2): T = T A ​ + 5 T B ​ − T A ​ ​ = 5 4 T A ​ + T B ​ ​ .

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