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Railway lines are laid with gaps to allow for expansion . The gap between two lines is 0.5 cm at `10^@C` and the length of a line is 12m . At what temperature will be lines just touch ?
`alpha = 11 xx 10^(-6)//^@C` .

Text Solution

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The lines will touch when each line expands by 0.25 cm at either end 0.5 cm at both ends.
From the formula `l_2 - l_1 = l_1 alpha(t_2 - t_1) , t_2 = (l_2-l_1)/(l_1 alpha) + t_1`
`= (0.5 xx 10^(-2))/(12 xx 11 xx 10^(-6) )+10`
= 37.8 + 10 = `47.8^@C`
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