InterviewSolution
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InterviewSolution
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Two metal rods of lengths `L_(1)` and `L_(2)` and coefficients of linear expansion `alpha_(1)` and `alpha_(2)` respectively are welded together to make a composite rod of length `(L_(1)+L_(2))` at `0^(@)C.` Find the effective coefficient of linear expansion of the composite rod.A. `(L_(1)alpha_(1)^(2)-L_(2)alpha_(2)^(2))/(L_(1)^(2)+L_(2)^(2))`B. `(L_(1)^(2)alpha_(1)-L_(2)^(2)alpha_(2))/(L_(1)^(2)+L_(2)^(2))`C. `(L_(1)alpha_(1)+L_(2)alpha_(2))/(L_(1)-L_(2))`D. `(L_(1)alpha_(1)+L_(2)alpha_(2))/(L_(1)+L_(2))` |
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Answer» Correct Answer - D Given, the length of rods are `L_(1) and L_(2)` Coefficient of linear expansions are `alpha_(1) and alpha_(2)` As we know that `DeltaL_(1)=alpha_(1)L_(1)DeltatrArrDeltaL_(2)=alpha_(2)L_(2)Deltat` and for combined rod `DeltaL=alpha(L_(1)+L_(2))Deltat` Now, `DeltaL=DeltaL_(1)+DeltaL_(2)` `rArr" "alpha(L_(1)+L_(2))Deltat=alpha_(1)L_(1)Deltat+alpha_(2)L_(2)Deltat` `rArr" "alpha(L_(1)+L_(2))Deltat=alpha_(1)L_(1)Deltat+alpha_(1)L_(2)` `rArralpha=(alpha_(1)L_(1)+alpha_(2)L_(2))/(L_(1)+L_(2))` |
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