A composite bar of length L $$=$$ $$L1+L2$$, is made up from a rod of material I and of length $$L1$$ attached to a rod of material $$2$$ and of length $$L2$$ as shown. If α$$1$$ and α$$2$$ are their respeclive coefficients of linear expansion, then equivalent coefficient of linear expansion for the composite rod is:

Question

A composite bar of length L $$=$$ $$L1+L2$$, is made up from a rod of material I and of length $$L1$$ attached to a rod of material $$2$$ and of length $$L2$$ as shown. If α$$1$$ and α$$2$$ are their respeclive coefficients of linear expansion, then equivalent coefficient of linear expansion for the composite rod is:

Infinity Learn · Accepted Answer

When it has been given a temperature change ∆T, the new length of the composite bar is the sum of the individual final lengths (Let$$ 'α' be required coefficient of linear $$expansion)L$$' $$=$$ L'$$1+L$$'$$2L(1+$$α∆$$T) $$=$$ $$L1(1+$$α$$1$$∆$$T)+L2(1+$$α$$2$$∆$$T)$$⇒L $$+$$ Lα∆T $$=$$ $$L1+L1$$α$$1$$∆T $$+$$ $$L2+L2$$α$$2$$∆T⇒$$L+L$$α∆T $$=$$ $$L+L1$$α$$1$$∆$$T+L2$$α$$2$$∆$$T($$∵ $$L1+L2$$ $$=$$ $$L)$$⇒ Lα∆T $$=$$ $$L1$$α$$1$$∆T $$+$$ $$L2$$α$$2$$∆T⇒α $$=$$ $$L1$$α$$1+L2$$α$$2L$$

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A composite bar of length L = L1+L2, is made up from a rod of material I and of length L1 attached to a rod of material 2 and of length L2 as shown. If α1 and α2 are their respeclive coefficients of linear expansion, then equivalent coefficient of linear expansion for the composite rod is:

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