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

Question

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

Infinity Learn · Accepted Answer

Using α $$=$$ ∆$$LL0$$.∆T α$$1$$ $$=$$ $$0.065030$$×$$100$$; α$$2$$ $$=$$ $$0.035030$$×$$100L01$$.α$$1$$.∆T $$+L02$$.α$$2$$.∆T $$=$$ $$0.0580and$$ $$L01+L02$$ $$=$$ $$30Solving$$ $$L01$$ $$=$$ $$23$$ cm

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