The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by 100 is: (For steel Young's modulus is 2 × 10¹¹ Nm⁻² and coefficient of thermal expansion is 1.1 × 10⁻⁵ K⁻¹) (a) 2.2 × 10⁸ Pa (b) 2.2 × 10⁹ Pa (c) 2.2 × 10⁷ Pa (d) 2.2 × 10⁶ Pa

Answer: (a). Thermal stress = YαΔ T (independent of length). = 2 × 10¹¹ × 1.1 × 10⁻⁵ × 100 = 2.2 × 10⁸ Pa So the answer is (a) 2.2 × 10⁸ Pa.

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Q16JEE Main 2014Easy

Thermal Stress & Breaking Stress

The pressure that has to be applied to the ends of a steel wire of length $10\text{ cm}$ to keep its length constant when its temperature is raised by $100^\circ\text{C}$ is: (For steel Young's modulus is $2 \times 10^{11}\text{ Nm}^{-2}$ and coefficient of thermal expansion is $1.1 \times 10^{-5}\text{ K}^{-1}$ )

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Answer: (a)

Thermal stress $= Y\alpha\Delta T$ (independent of length).
$= 2 \times 10^{11} \times 1.1 \times 10^{-5} \times 100 = 2.2 \times 10^8\text{ Pa}$
So the answer is (a) $2.2 \times 10^8\text{ Pa}$ .

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