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

A steel wire of length 20 cm and uniform cross-section `1mm^(2)` is tied rigidly at both the ends. If the temperature of the wire is altered from `40^(@)C` to `20^(@)C`, the change in tension. [Given coefficient of linear expansion of steel is `1.1xx10^(5) .^(@)C^(-1)` and Young's modulus for steel is `2.0xx10^(11) Nm^(-2)`]

A

10 N

B

20 N

C

40 N

D

60 N

Text Solution

Verified by Experts

The correct Answer is:
C
`:. Y = (FL)/(Al) :. F = (Yal)/(L)`
but increase in length `l = L prop Delta theta`
`:. F = (YA L prop Delta theta)/(L) = YA prop Delta theta`
`:. F = 2 xx 10^(11) xx 1 xx 10^(-6) xx 10^(-5) xx 20 = 40 N`
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