A steel rod of length 1 m and cross sectional area 10⁻⁴ m² is heated from 0° C to 200° C without being allowed to extend or bend. The compressive tension produced in the rod is ___________ × 10⁴ N. (Given Young's modulus of steel =2 × 10¹¹ Nm⁻², coefficient of linear expansion =10⁻⁵ K⁻¹ )

Solution

Physics sir · 4 steps

The rod wants to expand but the walls push it back, so the thermal strain becomes an elastic strain.

1. Strain it is denied. If the rod were free, it would grow by Δ L = LαΔ T. The supports stop it, so they compress it by exactly that much. The strain is (Δ L)/L = αΔ T, and the length L drops out.
2. Stress and force. By Hooke's law the stress is YαΔ T. Force is stress times area.

   F = YAαΔ T = (2 × 10¹¹)(10⁻⁴)(10⁻⁵)(200) N

3. Put in numbers. 2 × 10¹¹ × 10⁻⁴ = 2 × 10⁷. Multiply by 10⁻⁵ to get 200, then by 200 to get 4 × 10⁴ N.
4. So. The compressive force is 4 × 10⁴ N, so the blank is 4.

The common slip: 40000. Writing the full force, 40 000 N, gives 40000. The blank already carries the × 10⁴, so the entry is 4.

The idea to keep. A rod clamped at both ends and heated feels thermal stress YαΔ T, whatever its length. Multiply by the area only when the question asks for force.

Answer from the NTA final answer key. Solution by PrepWiser.