Practice portal › Thermal Properties of Matter › Thermal Stress and Applications of Expansion

A steel rail of length 5 m and area of cross-section 40 cm² is prevented from expanding along its length while the temperature rises by 10 °C. If the coefficient of linear expansion and Young's modulus of steel are 1.2×10⁻⁵ K⁻¹ and 2×10¹¹ N m⁻² respectively, the force developed in the rail is approximately

Asked in JEE Main Online 2017 · Thermal stress and strain

• (1) 2×10⁹ N
• (2) 3×10⁻⁵ N
• (3) 2×10⁷ N
• (4) 1×10⁵ N

Step-by-step solution

Why the other options are wrong

• (1) comes from no consistent slip lands here; it is a filler four decades above the key. The route worth checking, leaving the area in cm² so that A=40, gives 9.6×10⁸ N, which is not this number either.
• (2) comes from is a strain-sized number wearing newtons. It is close to αΔ T=1.2×10⁻⁴, the dimensionless strain, which is what you get by never multiplying by Y or A at all.
• (3) comes from is the *stress* YαΔ T=2.4×10⁷ Pa reported as a force; the area 40 cm²=4×10⁻³ m² was never applied. Stress is in pascals, force in newtons.

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.