A brass rod, 4.0 m long and with a cross sectional area of 9.2 × 10^-⁶ m² is subjected to a tension of 6.0 × 10³ N/m². The Young's modulus for brass is 9.0 × 10¹⁰ N/m², and the Poisson ratio is 0.48. By how much does the volume of the rod change? A)6.3 × 10^-⁷ m³ B)0.029 m³ C)2.7 × 10^-⁷ m³ D)4.0 × 10^-⁷ m³ E)5.2 × 10^-⁷ m³

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Quizplus · Accepted Answer

The change in volume is given by:$$\Delta V = - \frac{1}{3} \beta Y A L \epsilon$$where:$$\beta$$ is the Poisson ratioY is the Young's modulusA is the cross-sectional areaL is the length$$\epsilon$$ is the strainSubstituting the given values, we get:$$\Delta V = - \frac{1}{3} (0.48)(9.0 	imes 10^{10} N/m^2)(9.2 	imes 10^{-6} m^2)(4.0 m)(6.0 	imes 10^3 N/m^2)$$$$\Delta V = -5.2 	imes 10^{-7} m^3$$

A Brass Rod, 4