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 mid point of the wire. The strain produced in the wire, (if the vertical distance through which the mid point of the wire moves down $x\

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 mid point of the wire. The strain produced in the wire, (if the vertical distance through which the mid point of the wire moves down $x\ < l$) will be

Dr. Abubacker · Accepted Answer

(c) From figure the increase in length $\mathrm{\Delta}l = (PR + RQ) - \ PQ\ $
= 2PR – PQ
= $2\left( l^{2} + x^{2} ight)^{1/2} - 2l = 2l\left( 1 + \frac{x^{2}}{l^{2}} ight)^{1/2} - 2l$
= $2l\left\lbrack 1 + \frac{1}{2}\frac{x^{2}}{l^{2}} ightbrack - 2l$
= $x^{2}/l$ ( By Binomial theorem)
$	herefore\ \ \ \ \ Strain = \ \mathrm{\Delta}l/2l$ = $x^{2}/2l^{2}$
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Explanation

Reviewed by Dr. Abubacker

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