An iron rod of length 50 cm is joined at an end to an aluminium rod of length 100 cm . All measurements refer to 20 ° C . The coefficients of linear expansion of iron and aluminium are 12× 10- 6 ° C- 1 and 24× 10- 6 ° C- 1 respectively. The average coefficient of expansion of the composite system is

Question

An iron rod of length 50 cm is joined at an end to an aluminium rod of length 100 cm . All measurements refer to 20 ° C . The coefficients of linear expansion of iron and aluminium are 12× 10- 6 ° C- 1 and 24× 10- 6 ° C- 1 respectively. The average coefficient of expansion of the composite system is (A) 36 × 10-6 ° C -1 (B) 12 × 10-6 ° C -1 (C) 20 × 10-6 ° C -1 (D) 48 × 10-6 ° C -1

Tardigrade Admin · Accepted Answer

Length of iron rod at 100oC, L1 = 50[1 + 12 x 10-6 x (100 - 20)] = 50.048 cm Length of aluminum rod at 100oC, L2 = 100[1 + 24 x 10-6 x (100 - 20)] = 100.192 cm The length of composite system at 20oC = 50 + 100 = 150 cm and length of composite system at 100oC = 50.048 + 100.192 = 150.24 cm â´ A verage α = ( text0.24 cm/1 5 0 cm × (1 0 0 - 2 0)) = 20 x 10-6/oC

$36 \times 1 0^{- 6}^{\circ} C^{- 1}$

$12 \times 1 0^{- 6}^{\circ} C^{- 1}$

$20 \times 1 0^{- 6}^{\circ} C^{- 1}$

$48 \times 1 0^{- 6}^{\circ} C^{- 1}$

36×10−6∘C−1

12×10−6∘C−1

20×10−6∘C−1

48×10−6∘C−1

$36 \times 1 0^{- 6}^{\circ} C^{- 1}$

$12 \times 1 0^{- 6}^{\circ} C^{- 1}$

$20 \times 1 0^{- 6}^{\circ} C^{- 1}$

$48 \times 1 0^{- 6}^{\circ} C^{- 1}$