Two metal rods of lengths $$L1$$ and $$L2$$ and coefficients of linear expansion α$$1$$ and α$$2$$ respectively are welded together to make a composite rod of length (L1$$ $$+$$ $$L2) at $$0$$°C. Find the effective coefficient of linear expansion of the composite rod. [EAMCET $$2015$$]

Question

Two metal rods of lengths $$L1$$ and $$L2$$ and coefficients of linear expansion α$$1$$ and α$$2$$ respectively are welded together to make a composite rod of length (L1$$ $$+$$ $$L2) at $$0$$°C. Find the effective coefficient of linear expansion of the composite rod. [EAMCET $$2015$$]

Infinity Learn · Accepted Answer

Given, the lengths of rods are $$L1$$ and $$L2and$$ coefficients of linear expansions are α$$1$$ and α$$2$$.As, ∆$$L1$$ $$=$$ α$$1L1$$∆t   and  ∆$$L2$$ $$=$$ α$$2L2$$∆tand for combined rod,                              ∆L $$=$$ α (L1+L2)∆tNow,                      ∆L $$=$$ ∆$$L1+$$∆$$L2$$⇒       α (L1+L2) ∆t $$=$$ α$$1L1$$∆t $$+$$ α$$2$$ $$L2$$∆t⇒            α (L1+L2) $$=$$ α$$1L1$$ $$+$$ α$$2L2$$⇒                                 α $$=$$ α$$1L1$$ $$+$$ α$$2L2L1+L2$$

Two metal rods of lengths L₁ and L₂ and coefficients of linear expansion $α_{1}$ and $α_{2}$ respectively are welded together to make a composite rod of length (L₁ + L₂) at 0°C. Find the effective coefficient of linear expansion of the composite rod. [EAMCET 2015]

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Two metal rods of lengths L1 and L2 and coefficients of linear expansion α1 and α2 respectively are welded together to make a composite rod of length (L1 + L2) at 0°C. Find the effective coefficient of linear expansion of the composite rod. [EAMCET 2015]

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Two metal rods of lengths L₁ and L₂ and coefficients of linear expansion $α_{1}$ and $α_{2}$ respectively are welded together to make a composite rod of length (L₁ + L₂) at 0°C. Find the effective coefficient of linear expansion of the composite rod. [EAMCET 2015]