Question

An iron rod of length 70 cm is joined at one end to an aluminium rod of length 130 cm. All measurements refer to 30° C. Find the average coefficient of linear expansion at 150°C. The coefficient of linear expansion of iron and aluminium are 12 × 10 ^{- 6}/°C and 24 × 10 ^{- 6}/°C respectively.
1. 20.2 × 10 ^{- 6}/°C
2. 18 × 10 ^{- 6}/°C
3. 19.8 × 10 ^{- 6}/°C
4. 12 × 10 ^{- 6}/°C

Answer 1

Correct Answer - Option 3 : 19.8 × 10 ^{- 6}/°C

The length of iron rod at 150°C is

L_iron = L_o (1 + αθ)

= 70[1 + 12 × 10 ^{- 6} × (150 - 30)] = 70.1008 cm

Length of aluminium rod at 150°C

l_Al = 130 (1 + 24 × 10 ^{- 6} × (150 - 30)) = 130.3744 cm

The length of composite system at 150°C is

70.1008 + 130.3744 = 200.4752 cm

Average coefficient of linear expansion

\(\alpha = \frac{{200.4752 - 200}}{{200\; \times \;\left( {150 - 30} \right)}}\) = 1.98 × 10 ^{- 5}/°C

= 19.8 × 10 ^{- 6}/°C