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Q.

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

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a

3.8×10² N

b

5.8×10² N

c

7.8×10² N

d

6.8×10² N

answer is A.

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Detailed 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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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