Question

If the temperature of a rod of length L is increased by T° C, whose coefficient of linear expansion is α and Young’s modulus is E, then free expansion of the rod due to increase in temperature is given by which of the following expressions? 
1. αTE²L 
2. αT/L 
3.  αT/E 
4. None of the above

Answer 1

Correct Answer - Option 4 : None of the above

Concept

As the rod is free it expands or contracts when subjected to temperature change

Given,

Temperature difference = T° C

Coefficient of linear expansion (α)

Young’s modulus (E)

Length of the rod is 'L'

Increase in length (δl ) is given by 

\(\delta l = L \times \alpha \times T\)

∴None of the above option

Strain is  

\(strain = \frac{{\delta l}}{L} = \frac{{L \times \alpha \times T}}{L} = \alpha \times T\)

Note: When rods are free to expand or contract, there is no thermal stresses developed