A uniform wire of length l of weight w is suspended from the roof with a weight of W at the other end. The stress in the wire at l 3 distance from the top is ( W A + 2 w A ) , where, A is the cross sectional area of the wire. The value of is _______.

Step-by-step solution

Let T be the tension in the wire at a distance l 3 from the top. The length of the wire below this point is l - l 3 = 2l 3 . The weight of this lower part of the wire is w l 2l 3 = 2w 3 . The total downward force (tension T ) at this point is the sum of the weight W attached at the bottom and the weight of the lower part of the wire: T = W + 2w 3 The stress at this point is given by the tension divided by the cross-sectional area A : Stress = T A = W + 2w 3 A = W A + 2 3 w A Comparing this with the given expression