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 ${(2mm}^{2})$ were taken and curves between extension and load were obtained. The slope of the curves were plotted with (extension/ load) along $y$ axis and the wire length along $x$ axis. If the young’s modulus of given steel wires $x \times 10^{9} {Nm}^{- 2}$ , then the value of x is

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Detailed Solution

$Slope = \frac{Y}{x} = \frac{Δ L / F}{L} = \tan θ = \frac{0.25 \times 10^{- 3}}{1}$

$\frac{Δ L}{FL} = 0.25 \times 10^{- 3} = \frac{1}{4 \times 10^{- 3}}$

$\frac{FL}{Δ L} = 4 \times 10^{3}$

$Y = \frac{FL}{A Δ L} = \frac{4 \times 10^{3}}{2 \times 10^{- 6}} = 2 \times 10^{9} N / m^{2}$

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