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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°C is: (For steel Young's modules is 2 × 10¹¹ N m⁻² and coefficient of thermal expansion is 1.1 × 10⁻⁵ K⁻¹)

1. 2.2 × 10⁹ Pa
2. 2.2 × 10⁷ Pa
3. 2.2 × 10⁶ Pa
4. 2.2 × 10⁸ Pa

Correct answer: 2.2 × 10⁸ Pa

Solution

The correct option is derived from the formula for thermal stress, which accounts for the change in temperature and the material's properties. By applying the Young's modulus and the coefficient of thermal expansion, we find that the pressure needed to maintain the wire's length at a higher temperature is 2.2 × 10⁸ Pa.

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