Calculate the pressure needed at the ends of a steel wire (length 10text cm ) to keep its length unchanged if the temperature is increased by 100^ circ text C . (Given: Steel Young's modulus Y = 2 times 10^ 11 text Nm ^ -2 and coefficient of linear expansion alpha = 1.1 times 10^ -5 text K ^ -1 ) [cite: 430, 431]

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EEJ MAIN Physics QUESTION #7097

Question 1

Calculate the pressure needed at the ends of a steel wire (length $10\text{ cm}$) to keep its length unchanged if the temperature is increased by $100^{\circ}\text{C}$. (Given: Steel Young's modulus $Y = 2 \times 10^{11}\text{ Nm}^{-2}$ and coefficient of linear expansion $\alpha = 1.1 \times 10^{-5}\text{ K}^{-1}$) [cite: 430, 431]

$2.2 \times 10^{7}\text{ Pa}$
$2.2 \times 10^{6}\text{ Pa}$
$2.2 \times 10^{8}\text{ Pa}$✔️
$2.2 \times 10^{9}\text{ Pa}$

Correct Answer Explanation

Thermal stress is the pressure required to prevent expansion and is given by:

$\text{Stress} = Y \alpha \Delta \theta$ [cite: 431]
$\text{Stress} = (2 \times 10^{11}) \times (1.1 \times 10^{-5}) \times 100$ [cite: 430, 431]
$\text{Stress} = 2.2 \times 10^{8}\text{ Pa}$

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