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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

For 'A',αA=∆lAlA∆T=0.07520(100) For 'B',αB=∆lBlB∆T=0.04520(100) For composite rod,  ∆l=αAlA∆T+αB(20-lA)∆T ⇒                 0.060=0.07520lA+0.04520(20-lA) ⇒                          lA=10 cm
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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