An iron bar of length l and cross-section A is heated from 0°C to 100°C. If the rod is so held that it is not permitted to expand or bend, the force developed in it is :

Options

A. directly proportional to length
B. inversely proportional to length
C. independent of length
D. inversely proportional to area of cross-section

Answer

C

Explanation

Change in length `Deltal=alDeltaT`
Stress = `F/A` and Strain= `(Deltal)/l`
Now Y =`F/Axxl/(Deltal)=F/Axxl/(alphalDeltaT)` or` ~F=YalphaADeltaT`
Clearly F does not depend upon length. Hence the correct choice is (c).