1. Tardigrade
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  4. A wire of cross-sectional area A is stretched horizontally between two clamps loaded at a distance 2l 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

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Q. A wire of cross-sectional area $A$ is stretched horizontally between two clamps loaded at a distance $2l$ 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

NTA AbhyasNTA Abhyas 2020

Solution:

From figure the increase in length $\Delta l=\left(P R + R Q\right)- \, PQ$
= 2PR - PQ
$=2\left(l^{2} + x^{2}\right)^{1 / 2}-2l=2l\left(1 + \frac{x^{2}}{l^{2}}\right)^{1 / 2}-2l$
$=2l\left[1 + \frac{1}{2} \frac{x^{2}}{l^{2}}\right]-2l$ ( By Binomial theorem)
$=x^{2}/l$
$\therefore \, \, Strain= \, \Delta l/2l=x^{2}/2l^{2}$

Solution