In an experiment to determine the Young's modulus, steel wires of five different lengths (1,2,3,4 and 5 m) but of same cross section (2mm2) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with the wire length and the following graph is obtained. If the Young's modulus of given steel wires is x×1011Nm−2, then the value of x is ______.
Answer: 2
Solution
From the graph, the slope of the line (extension/load vs length) is 0.25×10−5 m/N. For a wire under tension, WΔl=YAL, so the slope =YA1. Therefore Y=(slope)×A1=0.25×10−5×2×10−61=0.5×10−111=2×1011 N/m². Thus x=2.
