Question

A metal rod is fixed rigidly at two ends . If $L,\alpha$ and $Y$ respectively denote the length of the rod, coefficient of linear thermal expansion and Young's modulus of its material, then for an increase in temperature of the rod by $△T$, the longitudinal stress developed in the rod is

• A. Inversely proportional to $\alpha$
• B. Inversely proportional to $Y$
• C. Directly proportional to $\frac{△T}{Y}$
• D. Independent of $L$

Answer 1

The correct option is D Independent of $L$

The increase in length of the rod due to increase in temperature of the rod=$L\alpha \Delta T$

The strain in the rod due to increase in temperature of the rod=$\alpha \Delta T$

Hence the longitudinal stress in the rod=$Y\times Strain=Y\alpha \Delta T$

Hence correct answer is option D.