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Question

A uniform rope of mass M and length L is accelerated upwards with acceleration a by applying force on the topmost point. What is the tension in the rope at a distance X from the lower end?


Your Answer
A
ML×a
Correct Answer
B
MLX(g+a)
Your Answer
C
ML(LX)a
Your Answer
D
None

Solution

The correct option is B MLX(g+a)
We assume the tension T at distance X from lower end. Mass of the lower portion of length X is m.
Since the rope is uniform, therefore mass per unit length remains same for every section.
m=(ML)X

F.B.D of lower portion.


Tmg=ma
T=m(g+a)
T=MLX(g+a)

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