A steel wire of length 20 cm and uniform cross section `1 mm^(2)` is tied rigidly at both the ends. If temperature of the wire is altered from `40^(@)C` to `20^(@)C`, calcutlate the change in tension. Given coefficient of linear expansion of steel is `1.1 xx 10^(-5) ^(@)C^(-1)` and Young's modulus for steel is `2.0 xx 10^(11) Nm^(-2)`.

Explanation

The change in tension in the steel wire is due to restoring force set up in the wire, when temperature of the wire is lowered.
When wire is coooled by temperature `Delta theta` the change in the wire of length l is
`Delta l = l alpha Delta theta or (Delta l)/(l) = alpha Delta theta`
Change in the tension in the wire when it is cooled is given by
`F = YA Delta l//l = Y A alpha Delta theta`
`=(2.0 xx 10^(11)) xx (1 xx 10^(-6)) xx (1.1 xx 10^(-5)) xx (40^(@) - 20^(@))`
`=44N`.