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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 1.5×105/ 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 1.2×105/ C
Given:
For rod AB,
Coefficient of thermal expansion, αAB=1.5×105/ 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
α1Y
[ Temperature difference, compressive force and area of cross section are constant and equal for both rods]
So, αABαBC=YBCYAB
Substituting values, 1.5×105αBC=1.5×10111.2×1011
αBC=1.2×105/ C

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