A steel rod is rigidly clamped at its two ends. The rod is under zero tension at `20^@C`. If the temperature rises to `100^@ C`, what force will the rod exert on one of the clapms? Area of cross section of the rod `= 2.00 mm^2` . Coefficient of linear expansion of steel `= 12.0 xx 10^(-6)C^(-1)` and Young's modulus of steel `2.00 xx 10^(11) N m^(-2)`.

Explanation

`theta_1= 20^@C` , theta_2= 100^@C`
`A= 2 mm^2 = (2 xx (10^-6) (m^2))`
` (alpha_steel) = (12 xx 10^-6 /(^@C)`
`Y_steel = (2 xx (10^11N))/(m^2)`
Force exerted on th clamps = ?
`(F/A) / strain = Y `
` F= (Y xx (Delta L))/ L xx A `
` = (YL alpha Delta theta A) / L = ( YA alpha Delta theta)`
` =2 xx 10^11 xx 2 xx 10^-6 xx 12`
` xx 10^-6 xx 80`
` = 48 xx 80 xx 10^-1 = 384N`