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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.]

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answer is 1.41.

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Detailed Solution

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

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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.]