A wire, 3 m in length and 1 mm in diameter at 30° C is kept in low temperature at -170° C and is stretched by hanging a weight of 10 kg at one end. The change in length of the wire is [Y = 2 x 10 11 Nm -2 , g = 10 ms -2 and a = 1.2 x 10 -5 /°c]
Text Solution
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5. 2 mm
The change in length of the wire due to change in temperature
= 
LT = 1.2 x 10 5 x 3 x (-170 - 30)
= -7.2 x 10 -3 m
The change in the length of the wire due to the stretching force
The total change in the length of the wire
= -7.2 x 10 -3 + 2 x 10 -3
= -5.2 x 10 -3 m = -5. 2 mm
The negative sign indicates contraction of the wire
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