A) \[\frac{{{\ell }_{1}}}{{{\ell }_{2}}}\,\,=\,\,\frac{{{\alpha }_{1}}}{{{\alpha }_{2}}}\]
B) \[\frac{{{\ell }_{1}}}{{{\ell }_{2}}}\,\,=\,\,\frac{{{\alpha }_{2}}}{{{\alpha }_{1}}}\]
C) \[\ell _{2}^{2}{{\alpha }_{1}}\,\,=\,\,\ell _{1}^{2}{{\alpha }_{2}}\]
D) \[\frac{\alpha _{1}^{2}}{{{\ell }_{1}}}=\frac{\alpha _{2}^{2}}{{{\ell }_{2}}}\]
Correct Answer: B
Solution :
\[\Delta {{\ell }_{1}}\,=\,\,{{\ell }_{1}}{{\alpha }_{1}}\Delta T\] \[\Delta {{\ell }_{2}}\,=\,\,{{\ell }_{2}}{{\alpha }_{2}}\Delta T\] \[\frac{{{\ell }_{1}}}{{{\ell }_{2}}}=\frac{{{\alpha }_{2}}}{{{\alpha }_{1}}}\,\,for\,\,temperature\,\,independence\]You need to login to perform this action.
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