Q158 / 200 · WBJEE 2014 · Physics

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

  • A
    inversely proportional to $\alpha$
  • B
    inversely proportional to Y
  • Correct answer
    C
    directly proportional to $\Delta T / Y$
  • D
    independent of $L$

Solution

Strain $=\alpha \cdot \Delta T$ Stress $Y \propto \Delta T$ where $L=$ length of the rod $\boldsymbol{\alpha}=$ coefficient of linear thermal expansion $Y=$ Young's modulus of its material So, the longitudinal stress developed in the rod is directly proportional to $\frac{\Delta T}{Y}$

Hence, the correct answer is option: 'C'.

More Mechanical Properties of Solids Questions