Question

1

Homework Questions
A rod is held between two rigid supports. As the temperature rises a stress is developed in the rod. This force is
directly proportional to the length of the rod
(b) inversely proportional to the length of the rod
(c) directly proportional to the anea of cross-section
(d) independent of length and area of cross-section
​

Answer 1

Explanation:

force depend upon young modulus of rod and it's thermal expansion. so it is independent of length and area of cross-section of rod.

Answer 2

Length of the rod as a function of temperature         L′=L(1+αΔT)

where  α is the coefficient of thermal expansion.

            ΔT is the change in temperature

∴     ΔL=L′−L=LαΔT

Strain      LΔL=αΔT                      ............(1)

From Hooke's law,             Y=StrainStress         ⟹Stress=Y×Strain

∴  Stress  =Y×αΔT

⟹  Stress is independent of L

HOPE THIS WILL HELP YOU......