Question

# The lengths of steel and copper rods are so that the length of the steel rod is 5 cm longer than that of the copper rod at all temperatures, then length of each rod, are (α for copper = 1.7 × 10−5/∘C and α for steel = 1.1 × 10−5/∘C) -

A

9.17 cm; 14.17 cm

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B

9.02 cm; 14.20 cm

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C

9.08 cm; 14.08 cm

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D

9.50 cm; 14.50 cm

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Solution

## The correct option is A 9.17 cm; 14.17 cm Let LS and LC be the lengths of the steel and copper rods, and αS and αC be their coefficients of linear expansion respectively. When the rods are heated by ΔT∘C, the increases in lengths of the steel rod and the copper rod, are ΔLS = LSαSΔT, ΔLC = LCαCΔT. Given LS - LC = 5cm for all ΔT, LSαSΔT = LCαCΔt LSLC = αCαS = 1.7×10−51.1×10−5 LS = 17LC11. Using this in (LS−LC) = 5, and solving, we get LC = 9.17 cm. Therefore, LS = 5 + 9.17 = 14.17 cm. Hence (A) is correct

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