An iron rod of length 50 cm is joined at an end to an aluminum rod of length 100cm- All measurement refer to 20-C- Find the length of the composite system at 100-C and its average coefficient of linear expansion- The coefficient of linear expansion of iron and aluminum are 12 - 10-6-C and 24 - 10-6-C respectively-

The length of the iron rod at 100^∘C is The length of the aluminum rod at 100^∘C is l_2=(100 cm)[1+(24 × 10^ 6/^∘C)(100^∘C 20^∘C)] =100.192 cm The length ...

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Byju's Answer

Standard XIII

Physics

Thermal Expansion

An iron rod o...

Question

An iron rod of length 50 cm is joined at an end to an aluminum rod of length 100cm. All measurement refer to $20^{\circ} C$ . Find the length of the composite system at $100^{\circ} C$ and its average coefficient of linear expansion. The coefficient of linear expansion of iron and aluminum are $12 \times 10^{- 6} /^{\circ} C$ and $24 \times 10^{- 6} /^{\circ} C$ respectively.

50.24 c m, 10 \times 10^{- 6} /^{\circ} C

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160.24 c m, 120 \times 10^{- 6} /^{\circ} C

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150.24 c m, 20 \times 10^{- 6} /^{\circ} C

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250.5 c m, 25 \times 10^{- 6} /^{\circ} C

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Solution

The correct option is C $150.24 c m, 20 \times 10^{- 6} /^{\circ} C$
The length of the iron rod at $100^{\circ} C$ is
$T h e l e n g t h o f t h e a l u m i n u m r o d a t 100^{\circ} C i s l_{2} = (100 c m) [1 + (24 \times 10^{- 6} /^{\circ} C) (100^{\circ} C - 20^{\circ} C)] = 100.192 c m T h e l e n g t h o f c o m p o s i t e s y s t e m a t 100^{\circ} C i s 50.048 + 100.192 = 150.24 c m$
The length of the composite system at $20^{\circ} C$ is 150 cm. So, the average coefficient of linear expansion of the composite rod is
$α = \frac{0.24 c m}{150 c m \times (100^{\circ} C - 20^{\circ} C)} = 20 \times 10^{- 6} /^{\circ} C$

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