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A steel wire of length 20 cm and uniform...

A steel wire of length 20 cm and uniform cross-sectional area of `1 mm^(2)` is tied rigidly at both the ends at `45^(@)C`. If the temperature of the wire is decreased to `20^(@)C`, then the change in the tension of the wire will be
[Y for steel `= 2 xx 10^(11 Nm^(-2)`, the coefficient of linear expansion for steel `= 1.1 xx 10^(-5)//.^(@)CC^(-1)`]

A

22N

B

32N

C

55N

D

60N

Text Solution

Verified by Experts

The correct Answer is:
C
Coefficient of linear expansion `alpha = (dL)/(L(Delta T))`
`:. (Delta L)/(L) = alpha Delta T` …(1)
and `Y = (F.L)/(A.Delta L)`
`:. F = YA(Delta L)/(L) = Y A alpha Delta T` …from (1)
`:. F = 2 xx 10^(11) xx 1 xx 10^(-6) xx 1.1 xx 10^(-5) xx 25`
`:. F = 55 N`
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