Question

A flexible chain of weight $W$ hangs between two fixed points $A$ and $B$ 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 claim at the midpoint?

• A. $\frac{W}{2}cosec\theta$
• B. $\frac{W}{2}\tan \theta$
• C. $\frac{W}{2}\cos \theta$
• D. $\frac{W}{2}$

Answer 1

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

The flexible chain that has a weight $W$ hangs between two fixed points $A$ and $B$ which are at the same horizontal level$.$ The inclination of the chain with the horizontal at both the points of support is $\theta .$

the weight of the chain is a downward acting force at the centre of mass of the chain which lies at the mid point$.$ The tension in the chain is the same throughout the chain and is a force that equals the net force acting on the chain$.$ If the tension is $F,$ this can be divided into components in the horizontal direction and the vertical direction$.$ The force in the horizontal direction is $F\cdot \cos \theta$ this components cancels out$.$ The vertical component is equal to $2\cdot F\cdot \sin \theta$ and this is equal to the weight of the chain $W.$

$2\cdot F\cdot \sin \theta =W$

$\Rightarrow F=\frac{W}{2\cdot \sin \theta }$

$\Rightarrow F=\left(\frac{W}{2}\right)\cdot cosec\theta$

Hence,

option $\left(A\right)$ is correct answer.