Question

# A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If L,α 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 ΔT, the longitudinal stress developed in the rod is:

A
inversely proportional to α
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
inversely proportional to Y
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
directly proportional to ΔT/Y
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
independent of L
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

## The correct option is D independent of LLength 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=LαΔTStrain ΔLL=αΔT ............(1)From Hooke's law, Y=StressStrain ⟹Stress=Y×Strain∴ Stress =Y×αΔT⟹ Stress is independent of L

Suggest Corrections
0
Related Videos
Thermal Expansion
PHYSICS
Watch in App
Explore more