A rail track made of steel having length 410 mis clamped on a raillway line at its two ends ( Fig 11.3 ). On a summer day due to rise in temperature by 20^(@) C , it is deforned as shown in figure. Find x (displacement of the centre) if alpha_("steel") = 1.2 xx 10^(-5) //^(@)C

A rail track made of steel having length 410 mis clamped on a raillway

1.	A rail track made of steel having length 410 mis clamped on a raillway line at its two ends ( Fig 11.3 ). On a summer day due to rise in temperature by 20^(@) C , it is deforned as shown in figure. Find x (displacement of the centre) if alpha_("steel") = 1.2 xx 10^(-5) //^(@)C
Answer» SOLUTION :`x = SQRT(((L)/(2) + (Delta L)/(2))^(2) - ((L)/(2))^(2)) approx (1)/(2) sqrt(2L Delta L)` `Delta L = alpha L Delta t "" therefore x approx (L)/(2) sqrt(2 alpha Delta t)`