A steel wire of cross-sectional area $2 \times 10^{-5} m^{2}$is stretched through 2 mm by a force of 4000 N. Find the Young's modulus of the wire. The length of the wire is 2 m. $(2 \times 10^{11} Nm^{-2})$
Difficulty: Easy
Solution:
Cross-sectional area = A = $2 \times 10^{-5} m^{2}$
Extension =$\rho L = 2 mm = 2 \times$ $\frac{1}{1000}$ m = 0.002 m
Force = F = 4000 N
Length of the wire = L = 1m
Y =$\frac{FL}{(A\triangle L)}$
Y = $ \frac{(4000 \times 2)}{(2 \times10(^{3}) \times 0.002)}$ = $ \frac{8000}{0.004\times10^{-5}}$
Y =$\frac{800}{0.004 \times 10^{-5}}$
Y = $2,000,000 \times 10^{-5}$ $= 2 \times 10^{11} Nm^{-2}$
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