The ends \( Q \) and \( R \) of two thin wires, \( P Q \) and \( R ...

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The ends \( Q \) and \( R \) of two thin wires, \( P Q \) and \( R S \), are soldered (joined) together. Initially each of the wires has a
\( \mathrm{P} \) length of \( 1 \mathrm{~m} \) at \( 10^{\circ} \mathrm{C} \). Now the end \( P \) is maintained at \( 10^{\circ} \mathrm{C} \), while the end \( S \) is heated and maintained at \( 400^{\circ} \mathrm{C} \).
W The system is thermally insulated from its surroundings. If the thermal conductivity of wire \( P Q \) is twice that of the wire \( R S \) and the coefficient of linear thermal expansion of \( P Q \) is \( 1.2 \times 10^{-5} \mathrm{~K}^{-1} \), the change in length of the wire \( P Q \) is
[JEE 2016]
(a) \( 0.78 \mathrm{~mm} \)
(b) \( 0.90 \mathrm{~mm} \)
(c) \( 1.56 \mathrm{~mm} \)
(d) \( 2.34 \mathrm{~mm} \)
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