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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 tensionΔl=FlAY   ...(1)Increase in length due to rise in temperatureΔ=laΔt   ...(2) from (1) and (2) FlAY=lαΔt⇒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