Q 11-10-046JEE MainMedium
A $50$ cm long steel rod is clamped rigidly at both ends at $20°$C and then heated to $70°$C. Find the thermal stress produced, in units of $10^8$ Pa. ($Y = 2 \times 10^{11}$ Pa, $\alpha = 1.2 \times 10^{-5}\ °\text{C}^{-1}$)
Numerical value type. Enter your answer.
Answer: 1.2
Concept. The clamps prevent the expansion, so the thermal stress is $\sigma = Y\alpha\Delta T$ (independent of length).
Step 1. Substitute. $\Delta T = 50°$C:
$$\sigma = 2 \times 10^{11} \times 1.2 \times 10^{-5} \times 50 = 1.2 \times 10^8\ \text{Pa}$$
Answer. $1.2$.
Solution by Sreeraj P, M.Sc Physics