Find the work done in stretching a wire of cross-sectional area 10^{-2}\;cm^2 and 2\;m long through 0.1\;mm, if Y for the material of wires is 2\;*\;10^{11}\;N/m^2.
Given,
Cross-sectional area (A) = 10^{-2}\;cm^2 = 10^{-6}\;m^2
Length of wire (l) = 2\;m
Elongation of wire (e) = 0.1\;mm = 0.1 * 10^{-3}\;m
Young's modulus (Y) = 2 * 10^{11}\;N/m^2
Workdone (W) = ?
Cross-sectional area (A) = 10^{-2}\;cm^2 = 10^{-6}\;m^2
Length of wire (l) = 2\;m
Elongation of wire (e) = 0.1\;mm = 0.1 * 10^{-3}\;m
Young's modulus (Y) = 2 * 10^{11}\;N/m^2
Workdone (W) = ?
Y = \frac{F/A}{e/l} = \frac{F \;*\;l}{e \;*\; A}or,
F = \frac{Y.e.A}{l}Then,
Workdone (W) = \frac{1}{2}F.e = \frac{1}{2}\frac{Y.e^2.A}{l}
\;\;\;\; \;\;\;\; \;\;\;\; = \frac{1}{2} * \frac{2 \;*\; 10^{11}\;N/m^2 \;*\; (0.1 \;*\; 10^{-3})^2 \;*\; 10^{-6}}{2} = 5 * 10^{-4}\;J
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