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A uniform wire (Y=2xx10^11 N//m^2) is s...

A uniform wire `(Y=2xx10^11 N//m^2)` is subjected to a longitudinal tensile stress of `5xx10^(7) N//m^2`. If the overall volume change in the wire is 0.02% the fractional decrease in its radius is `5kxx10^(-6)` Find the value of k

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To solve the problem step by step, we will follow the given information and apply the relevant formulas. ### Step 1: Identify the given values - Young's modulus, \( Y = 2 \times 10^{11} \, \text{N/m}^2 \) - Longitudinal tensile stress, \( \sigma = 5 \times 10^{7} \, \text{N/m}^2 \) - Overall volume change, \( \Delta V/V = 0.02\% = 0.02/100 = 2 \times 10^{-4} \) - Fractional decrease in radius, \( \Delta r/r = 5k \times 10^{-6} \) ...
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