A 30.0 cm long metal rod expands by 0.0650 cm when its temperature is raised from 00C 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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a
23 cm
b
16 cm
c
18 cm
d
20 cm
answer is A.
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Detailed Solution
Using α = ∆LL0.∆T α1 = 0.065030×100; α2 = 0.035030×100L01.α1.∆T +L02.α2.∆T = 0.0580and L01+L02 = 30Solving L01 = 23 cm