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Question:

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

2.2×10⁶Pa

2.2×10⁸Pa

2.2×10⁷Pa

2.2×10⁹Pa

Solution:

We have change in length due to the change in temperature (considering no obstruction)
ΔL = αLΔT
or ΔL = 1.1×10⁻⁵ × 0.10 × 100 = 1.1×10⁻⁴m
Now pressure which needs to be applied would be given using
F/A = Pressure = ΔL × Y/L = 1.1×10⁻⁴ × 2 × 10¹¹/0.1 (Here ΔL is the expansion prevented)
= 2.2×10⁸Pa