A light rod of length $$200cm$$ is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of $$cross-section$$ $$0.1$$ sq.cm and the other is of brass of $$cross-section$$ $$0.2$$ sq.cm . Find the position along the rod at which a weight may be hung to produce (i) equal stresses in both wires and (ii) equal strains in both wires. $$Ybrass=10$$×$$1011dyne/cm2$$ and $$Ysteel=20$$×$$1011dyne/cm2$$

Question

A light rod of length $$200cm$$     is suspended from the ceiling horizontally by  means of two vertical wires of equal length tied to its ends. One of the  wires is made of steel and is of $$cross-section$$ $$0.1$$ sq.cm     and the other is of brass of $$cross-section$$ $$0.2$$ sq.cm     . Find the position along the rod at which a  weight may be hung to produce (i) equal stresses in both wires and (ii) equal  strains in both wires. $$Ybrass=10$$×$$1011dyne/cm2$$     and $$Ysteel=20$$×$$1011dyne/cm2$$

Infinity Learn · Accepted Answer

Stress same F∝A $$F1F2=A1A2=12$$⇒$$F2=2F1F1x=F2(2$$−$$x)F1x=2F1(2$$−$$x)$$⇒$$x=4$$−$$2x$$⇒$$x=1.333mx=133.3cmStrain$$ same: F∝$$AyF1F2=A1A2y1y2=0.20.1$$×$$10$$×$$101120$$×$$1011=1F1x=F2(2$$−$$x)$$⇒$$x=2-xx=1$$ $$m=100$$ cm

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