A steel wire of length 20 cm and unifrom crossection ` mm^(2)` is tied rigidly at both the ends. If temperature of the wre is altered from `40^(@)C` to `20^(@)C`, calcutlate the change in tension. Given coeffeicient 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 the wire of length l when wire is cooled by temperature `Delta theta` is given by
`Delta l = l alpha Delta theta or Delta l//l = alpha Delta theta`
Where `alpha` is the coeffiecient of linear expansion. Change in the tension of the wire when it is cooled is given by
`F=YA Deltal//l = YA alpha Delta theta`
`=(2.0 xx 10^(11)) xx (10^(-6)) xx (1.1 xx 10^(-5))`
`xx(40^(@)-20^(@))`
`44N`