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A block of weight 100N is suspended by copper and steel wires of same cross sectional area 0.5cm2 and, length 3m and 1m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are 30º and 60º, respectively. If elongation in copper wire is ΔlC and elongation in steel wire is ΔlS, then the ratio ΔlCΔlS is___[Young’s modulus for copper and steel are 1×1011N/m2 and 2×1011N/m2, respectively.]

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Detailed Solution

Horizontal, TScos⁡60=TCu cos⁡30⇒TS2=TCu32⇒TS=3TCU Vertical, TSsin⁡60+TCusin⁡30=100⇒3TCu×32+TCu2=100⇒2TCu=100⇒TCu=50N∴TS=3×50N Elongation in Cu wire ⇒ΔICu=ICuTCuAYCu Elongation in Steel wire ⇒ΔIS=ISTSAYS Ratio =ΔICΔIS=IcTCuAYCuIsTSAYsteel=YSICuTCuYCuISTS=2×3×501×3×50=2

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A block of weight 100N is suspended by copper and steel wires of same cross sectional area 0.5cm2 and, length 3m and 1m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are 30º and 60º, respectively. If elongation in copper wire is ΔlC and elongation in steel wire is ΔlS, then the ratio ΔlCΔlS is___[Young’s modulus for copper and steel are 1×1011N/m2 and 2×1011N/m2, respectively.]