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A 30.0 cm long metal rod expands by 0.0650 cm when its temperature is raised from $0^{0}$ C to 100°C. A second rod of different metal and of the same length expands by 0.0350 cm for the same rise in temperature. A third composite rod, also 30.0 cm long, is made-up of pieces of each of the above metals placed end to end and expands by 0.0580 cm when temperature is increased from O°C to 100°C. The length of the longer portion of the composite bar in cm at 0°C is

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20 cm

18 cm

23 cm

16 cm

answer is A.

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Detailed Solution

$Using α = \frac{∆ L}{L_{0} . ∆ T}$

$α_{1} = \frac{0.0650}{30 \times 100}; α_{2} = \frac{0.0350}{30 \times 100}$

$L_{01} . α_{1} . ∆ T + L_{02} . α_{2} . ∆ T = 0.0580$

and $L_{01} + L_{02} = 30$

Solving $L_{01} = 23 cm$

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