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Q.

What should be the lengths of a copper rod and a brass rod be at 0οC, so that the difference in the lengths of the copper and brass rods remains 10 cm at all temperatures? Given αb=1.8×10−5/K and αc=1.6×10−5/K.

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a

Lb=50cm, Lc=60 cm

b

Lb=100cm, Lc=110 cm

c

Lb=90cm, Lc=100 cm

d

Lb=80cm, Lc=90 cm

answer is D.

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Detailed Solution

Let the length of brass rod at 0oC is L∴ Length of copper rod at 0oC=L+10Since αcLc=αbLb,we can write, 1.6×10−5×L+10=1.8×10−5×L⇒L=80 cm∴ Length of copper rod =80+10cm=90 cm
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