A rail track made of steel having `20m` is clamped on a railway line at its two ends as show in Fig. `7(d). 17.` On a summer day due to rise in temperature by `22^(@)C`, it is deformed as show in Fig. `7(d). 17` .Find displacement of the center `(x)` . Given cofficient of liner expansion of steel is `1.2xx10^(-5) .^(@)C^(-1)`.

Answer

`[0.304 m]`

Explanation

From figure, `((L+Delta L)/(2))^(2)=x^(2)+(L//2)^(2)`
or `x=sqrt(((L+Delta L)/(2))^(2)-((L)/(2))^(2)`
`(1)/(2) sqrt(L^(2)+2L Delta L+Delta L^(2)-L^(2))`
`(1)/(2)sqrt(2 L Delta L)` `(therefore Delta L` is small quantity hence `Delta L^(2)` beng extermely small can be neglected)
Now, `Delta L=alpha L Delta T`
`:. x=(1)/(2)sqrt(2Lxxalpha L Delta T) =(L)/(2)sqrt(2alpha Delta T)`
`=(20)/(2)sqrt(2xx(2.1xx10^(-5))xx22)`
`=10xx30.39xx10^(-3)=0.304 m`