Question

# Two uniform rods AB and BC have Young's modulii 1.2×1011 N/m2 and 1.5×1011 N/m2 respectively. If coefficient of linear expansion of AB is 1.5×10−5/ ∘C and both have equal area of cross section, then coefficient of linear expansion of BC, for which there is no shift of the junction at all temperatures, is

A
1.5×105/ C
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B
1.2×105/ C
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C
0.6×105/ C
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D
0.8×105/ C
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Solution

## The correct option is B 1.2×10−5/ ∘CGiven: For rod AB, Coefficient of thermal expansion, αAB=1.5×10−5/ ∘C Young's modulus, YAB=1.2×1011 N/m2 For rod BC, Young's modulus YBC=1.5×1011 N/m2 Coefficient of thermal expansion, αBC=? For no shift of the junction at all temperatures, thermal strain should be countered by the compressive strain in the rods. ΔLL(thermal)=ΔLL(compressive) ⇒αLΔTL=FLAYL ⇒αΔT=FAY ⇒α∝1Y [ Temperature difference, compressive force and area of cross section are constant and equal for both rods] So, αABαBC=YBCYAB Substituting values, 1.5×10−5αBC=1.5×10111.2×1011 ⇒αBC=1.2×10−5/ ∘C

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