First slide

Thermal expansion

Question

A brass wire 1.8 m long at 27°C is held taut with little tension between the two rigid supports. If the wire is cooled to a temperature of -39°C , the tension developed in the wire, if its diameter is 2.0 mm, Coefficient of linear expansion of brass = 2.0×10^-5K^-1 ; Young’s modulus of brass = 0.91×10¹¹Pa

Moderate

A

3.8×10² N
B

5.8×10² N
C

7.8×10² N
D

6.8×10² N

Solution

Decrease in length due to tension
$Δl = \frac{Fl}{AY} . . . (1)$
Increase in length due to rise in temperature
$Δ = laΔt . . . (2)$
$from (1) and (2) \frac{Fl}{AY} = lαΔt \Rightarrow F = YAαΔT$

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