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_____x 10 4 N. (Given Young's modulus of steel = 2 x 10 11 N m -2 , coefficient of linear expansion = 10 -5 K -1 )
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The formula to calculate the Young's modulus of the material of the wire is given by
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The increase in length of the wire due to increase in temperature is given by
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Substitute the expression for the extension in length from equation into equation and simplify to obtain the required compressive tension.
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Substitute the values of the known parameters into equation to calculate the required compressive tension in the wire.
F=10 -4 m 2 x 10 -5 K -1 x 2 x 10 11 Nm -2 x (200° C - 0° C)
= 4 x 10 4 N
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