A steel rod of length 1 m and cross-sectional area is heated from to without being allowed to extend or bend. The compressive tension produced in the rod is _______ . (Given Young's modulus of steel , coefficient of linear expansion ) [2023

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Solution

Q.
A steel rod of length 1 m and cross-sectional area $10^{- 4} m^{2}$ is heated from $0 ° C$ to $200 ° C$ without being allowed to extend or bend. The compressive tension produced in the rod is _______ $\times 10^{4} N$ . (Given Young's modulus of steel $= 2 \times 10^{11} {Nm}^{- 2}$ , coefficient of linear expansion $= 10^{- 5} K^{- 1}$ ) [2023]

Ans.
(4)

$Stress = Y \times strain$

$Stress = Y \times \frac{Δ l}{l} = Y \times \frac{l α Δ T}{l} = Y α Δ T$

$Compressive Tension = Stress \times Area of cross section$

$= Y A α Δ T = 4 \times 10^{4} N$

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