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