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Question

A flexible chain of mass m hangs between two fixed points A and B at the same level. The inclination of the chain with the horizontal at the two points of support is θ. The tension at the midpoint C of the chain is

A
mgtanθ
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B
mg2tanθ
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C
Zero
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D
(mg)(sinθ+cosθ2)
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Solution

The correct option is B mg2tanθ
Let T be the tension in the chain at the ends and T be the tension in the chain at the midpoint C.
Resolve components of T in vertical and horizontal direction (as shown in the figure).


From the figure,
2Tsinθ=mg
Tension at the ends of the chain T=mg2sinθ

Now, consider the half portion of the hanging chain
At the midpoint C, tension in the chain is horizontal

T=TcosθT=mg2cotθ
or Tension at the mid-point C
=mg2tanθ

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