A wire of radius r stretched without tension along a straight line is lightly fixed at A and B as shown in fig. What is the tension in the wire when it ispulled into the shape A C B ? Assume Young's modulus of the material of the wire to be Y and d < l

From figure, the change in length=AC+CB−AB=2l2+d2−2l ∵AC=CB=l2+d2Let T be the tension in the wire. ThenLongitudinal stress =T/πr2and Longitudinal strain = Change in length  Original length  =2l2+d2−2l2l∴ Y=T/πr22l2+d2−2l/2l ,=Tlπr2l2+d2−lor T=Yπr2l2+d2−ll=Yπr21+d22l2…−1=Yπr2d22l2