Q 11-10-003NEETNEET 2024Top questionMedium
A metallic bar of Young's modulus, $0.5 \times 10^{11}\ \text{N m}^{-2}$ and coefficient of linear thermal expansion $10^{-5}\ °\text{C}^{-1}$, length $1$ m and area of cross-section $10^{-3}\ \text{m}^2$ is heated from $0°$C to $100°$C without expansion or bending. The compressive force developed in it is:
Answer: (D) $50 \times 10^3$ N
Concept. The bar is not allowed to expand, so the thermal strain $\alpha\Delta T$ is cancelled by an equal compressive strain: $F = YA\alpha\Delta T$.
Step 1. Substitute.
$$F = 0.5 \times 10^{11} \times 10^{-3} \times 10^{-5} \times 100 = 5 \times 10^4\ \text{N} = 50 \times 10^3\ \text{N}$$
(The length of the bar does not matter.)
Answer. $50 \times 10^3$ N (Option D).
Solution by Sreeraj P, M.Sc Physics