Question

A flexible chain of weight W hangs between two fixed points A & B which are at the same horizontal level. The inclination of the chain with the horizontal at both the points of support is $\theta$. What is the tension of the chain at the mid point?

• A. $\frac{W}{2}.cosec\theta$
• B. $\frac{W}{2}.tan\theta$
• C. $\frac{W}{2}.cot\theta$
• D. none

Answer 1

The correct option is A $\frac{W}{2}.cosec\theta$

Let the tension at the middle of the chain be T then:

weight of the chain is balanced by the vertical component of tension:

$\Rightarrow W=T\sin \theta +T\sin \theta$(Angle made with horizontal $=\theta$)

$\Rightarrow W=2T\sin \theta$

$\Rightarrow T=\frac{W}{2\sin \theta }=\frac{W}{2}cosec\theta$.