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Q.

A rod of length 20 cm is made of metal A. It expands by 0.075 cm when its temperature is raised from 0°C to 100°C. Another rod of a different metal B having the same length expands by 0.045 cm for the same change in temperature. A third rod of the same length is composed of two parts, one of metal A and the other of metal B. This rod expands by 0.060 cm for the same change in temperature. In the composite rod, the portion made of metal A has length

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a

12 cm

b

15 cm

c

10 cm

d

8 cm

answer is C.

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Detailed Solution

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$For' A', α_{A} = \frac{∆ l_{A}}{l_{A} ∆ T} = \frac{0.075}{20 (100)} For' B', α_{B} = \frac{∆ l_{B}}{l_{B} ∆ T} = \frac{0.045}{20 (100)} For composite rod, ∆ l = α_{A} l_{A} ∆ T + α_{B} (20 - l_{A}) ∆ T \Rightarrow 0.060 = \frac{0.075}{20} l_{A} + \frac{0.045}{20} (20 - l_{A}) \Rightarrow l_{A} = 10 cm$

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