Answer:
Yes. This is possible when the lengths of the rods are in inverse ratio of their coefficients of linear expansion. For the difference in the lengths of the two rods to remain same, \[\Delta {{l}_{1}}=\Delta {{l}_{2}}\] or \[{{l}_{1}}{{\alpha }_{1}}\Delta T={{l}_{2}}{{\alpha }_{2}}\Delta T\] or \[\frac{{{l}_{1}}}{{{l}_{2}}}=\frac{{{\alpha }_{2}}}{{{\alpha }_{1}}}.\]
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