# 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 1000C is :(For steel Young’s   modulus   is 2 x 1011 N m-2 and coefficient of thermal expansion is 1.1 x 10-5 K-1) Option 1) 2.2 x108 Pa Option 2) 2.2 x109 Pa Option 3) 2.2 x107 Pa Option 4) 2.2 x106 Pa

S SudhirSol

As we have learned

Thermal Strain -

$\frac{\Delta L}{L}=\alpha\; \Delta\; \theta$

- wherein

$\alpha=\frac{\Delta L}{L}\times \frac{1}{\Delta\; \theta}$

Thermal strain

$\frac{\Delta l }{l } - \alpha \Delta T\\ = 1.1 \times 10^{-5}\times 100\\ = 1.1 \times 10 ^{-3 }$

Thermal stess = Y strain

$= 2 \times 10 ^{11}\times 1.1\times 10^{-3}\\ = 2.2 \times 10^8N/m^2$

Pressure required = $2.2 \times 10 ^ 8 Pa$

Option 1)

2.2 x108 Pa

Option 2)

2.2 x109 Pa

Option 3)

2.2 x107 Pa

Option 4)

2.2 x106 Pa

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