A uniform metal bar of length 10 m with a crack at its midpoint is clamped between two rigid supports. The bar buckles upward due to temperature rise of `40^(@)C`. If the coefficient of linear expansion of the metal is `2.5 xx 10^(-6) .^(@)C^(-1)`, the maximum displacement of the mid-point of the bar is

Options

A. `11.3 cm`
B. `22.3 cm`
C. `33.3 cm`
D. `44.cm`

Answer

B

Explanation

Given, length of bar L = 10 m, rise in temperature, `Delta T = 40^(@)C` and coefficient of linear expansion, `alpha = 25 xx 10^(-6) .^(@)C^(-1)`
As, linear expansion,
`Delta L = L alpha Delta t = 10 xx 2.5 xx 10^(-6) xx 40`
`rArr Delta L = 0.1 cm`
In the figre below, let the displacement of mid point of bar is x.

Now, from `Delta OBA`,
`x = sqrt((AB)^(2) - (OA)^(2))`
`rArr x = sqrt(((10 + 0.001)/(2))^(2) - (5)^(2))`
`rArr x = 0.223 m`
Hence, `x = 22.3 cm`
Hence, the correct option is (b).