A bar with a crack at its centre buckles as a result temperature rise of 32^(0)C. If the fixed distance L_(0) is 3. 77m and the coefficient of linear expansion of the bar is 25 xx 10^(-6)//^(0) C find the rise x of the centre.(##AKS_NEO_CAO_PHY_XI_V01_PMH_C12_SLV_017_Q01.png" width="80%">

A bar with a crack at its centre buckles as a result temperature rise

1.	A bar with a crack at its centre buckles as a result temperature rise of 32^(0)C. If the fixed distance L_(0) is 3. 77m and the coefficient of linear expansion of the bar is 25 xx 10^(-6)//^(0) C find the rise x of the centre.(##AKS_NEO_CAO_PHY_XI_V01_PMH_C12_SLV_017_Q01.png" width="80%">
Answer» Solution :Consider one half of the BAR, its initial length `l_(0)= (L_(0))/(2)` Its length after increase in temperature `DELTA`t, `l = l_(0) (1 + alpha Delta T)` By PYTHOGORAS theorem `x^(2) = l^(2) - l_(0)^(2)` `l^(2) = l_(0)^(2) (1 + 2 alpha Delta T ) ` or x = `l_(0) sqrt(2 alpha Delta T)` = ` (3.77)/(2) sqrt(2(25 xx 10^(-6) xx 32)) = 7.5 xx 10^(-2) `m