Two rods one of aluminium of length ℓ1 having coefficient of linear expansion αa, and other steel of length ℓ2 having coefficient of linear expansion αs are joined end to end. The expansion in both the rods is same on variation of temperature. Then the value of is

Engineering

Physics

Thermal Expansion

Question

Two rods one of aluminium of length ℓ₁ having coefficient of linear expansion α_a, and other steel of length ℓ₂ having coefficient of linear expansion α_s are joined end to end. The expansion in both the rods is same on variation of temperature. Then the value of $\frac{l_{1}}{l_{1} + l_{2}}$ is

$\frac{α_{a} + α_{s}}{α_{s}}$

None of these

$\frac{α_{a}}{α_{a} + α_{s}}$

$\frac{α_{s}}{α_{a} + α_{s}}$

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$L_{1} α_{2} ΔT = L_{2} α_{s} ΔT$

$\frac{L_{1}}{L_{2}} = \frac{α_{s}}{α_{a}}$

$\frac{L_{1}}{L_{1} + L_{2}} = \frac{α_{s}}{α_{s} + α_{a}}$ .