A wire of cross-sectional area A is stretched horizontally between two clamps loaded at a distance 2 l metres from each other. A weight w kg suspended from the midpoint of the wire. The strain produced in the wire, (if the vertical distance through which the midpoint of the wire moves down x l ) will be

Question

A wire of cross-sectional area A is stretched horizontally between two clamps loaded at a distance 2 l metres from each other. A weight w kg suspended from the midpoint of the wire. The strain produced in the wire, (if the vertical distance through which the midpoint of the wire moves down x l ) will be, x 2 l 2, 2 x 2 l 2, x 2 2 l 2, x 2 l

MARKS App · Accepted Answer

From figure the increase in length ∆ l = P R + R Q - P Q = 2PR – PQ = 2 l 2 + x 2 1 / 2 - 2 l = 2 l 1 + x 2 l 2 1 / 2 - 2 l = 2 l 1 + 1 2 x 2 l 2 - 2 l ( By Binomial theorem) = x 2 / l ∴ S t r a i n = ∆ l / 2 l = x 2 / 2 l 2

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