Question

A heavy string of mass m hangs between two fixed points A and B at the same level. The tangents to the string at A and B are at an angle $\theta$ with the horizontal as shown in the figure. The tension in the string at the lowest point is

• A. $\frac{mg}{2sin\theta }$
• B. $\frac{mg}{2cos\theta }$
• C. $\frac{mg}{2tan\theta }$
• D. $\frac{mg}{2cot\theta }$

Answer 1

The correct option is C. $\frac{mg}{2tan\theta }$.

From the free body diagram of the half part of the wire shown above we have,

In the vertical direction, $Tsin\theta =mg/2$ .............(i)

(Since the tension at one end balances the weight of the half part of the wire)

In the horizontal direction, $T^{\prime }=Tcos\theta$ ...........(ii)

From equation (i) and equation (ii) we get,

$T^{\prime }=\frac{mg}{2}cot\theta =\frac{mg}{2tan\theta }$.