A) \[3{{\alpha }_{1}}{{\ell }_{2}}={{\alpha }_{2}}{{\ell }_{1}}\]
B) \[4{{\alpha }_{1}}{{\ell }_{2}}={{\alpha }_{2}}{{\ell }_{1}}\]
C) \[2{{\alpha }_{1}}{{\ell }_{2}}={{\alpha }_{2}}{{\ell }_{1}}\]
D) \[{{\alpha }_{1}}{{\ell }_{1}}={{\alpha }_{2}}{{\ell }_{2}}\]
Correct Answer: D
Solution :
[d] From question, \[({{\ell }_{2}}-{{\ell }_{1}})\] is maintained same at all temperatures hence changed in length for both rods should be same i.e., \[\Delta {{\ell }_{1}}=\Delta {{\ell }_{2}}\] As we know, coefficient of linear expansion \[\alpha =\frac{\Delta \ell }{{{\ell }_{0}}\Delta \ell }\] \[{{\ell }_{1}}{{\alpha }_{1}}\Delta T={{\ell }_{2}}{{\alpha }_{2}}\Delta T\Rightarrow {{\ell }_{1}}{{\alpha }_{1}}={{\ell }_{2}}{{\alpha }_{2}}\]You need to login to perform this action.
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