A rigid bar of mass $$15kg$$ is supported symmetrically by three wires each $$2$$ m long. The wires at each end are of copper and middle one is of iron. The ratio of the diameters of the copper to iron wire if each has the same tension is [Young's modulus of elasticity for copper and iron are $$100$$×$$109N/m2$$ and $$200$$×$$109N/m2$$ respectively.]

Question

A rigid bar of mass $$15kg$$ is supported symmetrically by three wires each $$2$$ m long. The wires at each end are of copper and middle one is of iron. The ratio of the diameters of the copper to iron wire if each has the same tension is [Young's modulus of elasticity for copper and iron are $$100$$×$$109N/m2$$ and  $$200$$×$$109N/m2$$ respectively.]

Infinity Learn · Accepted Answer

Each wire has same tension so each wire will have same extension to maintain horizontal position of bar. Also as they have same length, each wire will have same strain

$\begin{array}{l} Y = \frac{F l}{A Δ l} = \frac{F l}{π {(D / 2)}^{2} Δ l} = \frac{4 F l}{π D^{2} Δ l} \\ ∴ D^{2} \propto \frac{1}{Y} \\ ∴ \frac{D_{C u}}{D_{iron}} = \sqrt{\frac{Y_{iron}}{Y_{C u}}} = \sqrt{\frac{200 \times 10^{9}}{100 \times 10^{9}}} = \sqrt{2} = 1.41 \end{array}$

Elastic behaviour of solids

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Elastic behaviour of solids

Remember concepts with our Masterclasses.

Each wire has same tension so each wire will have same extension to maintain horizontal position of bar. Also as they have same length, each wire will have same strainY=FlAΔl=Flπ(D/2)2Δl=4FlπD2Δl​∴ D2∝1Y​∴ DCuDiron =Yiron YCu=200×109100×109=2=1.41

Ready to Test Your Skills?

free study material