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PhysicsNEET 2024Thermal expansion and calorimetry

Thermal Properties of Matter

A metallic bar of Young's modulus 0.5×1011 N m−20.5 \times 10^{11}\ \mathrm{N\,m^{-2}} and coefficient of linear thermal expansion 10−5 ∘C−110^{-5}\ ^\circ\mathrm{C}^{-1}, length 1 m and area of cross-section 10−3 m210^{-3}\ \mathrm{m^2}, is heated from 0∘0^\circC to 100∘100^\circC without expansion or bending. The compressive force developed in it is:

  1. A.50×10350 \times 10^{3} N✓
  2. B.100×103100 \times 10^{3} N
  3. C.2×1032 \times 10^{3} N
  4. D.5×1035 \times 10^{3} N

Solution

Thermal strain prevented =αΔT=10−5×100=10−3= \alpha\Delta T = 10^{-5} \times 100 = 10^{-3}. Force =YAαΔT=0.5×1011×10−3×10−3=5×104= Y A \alpha\Delta T = 0.5\times10^{11} \times 10^{-3} \times 10^{-3} = 5\times10^4 N =50×103= 50\times10^3 N.

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