Question

A rod of a material, of length L and radius r, initially at to room temperature, is held between two rigid supports so that its length does not change with changes in temeperature. The coefficient of linear expansion and the Young’s modulus, of the material of the rod, are α and Y, respectively. 

When the temperature of the rod increases by t°C, the stress, developed in it, would equal

(1) Y/(αt)

(2) (Yαt)

(3) (Yαt) (πr²)

(4) (Yαt)/(πr²)

Answer 1

(2) (Yαt)

When the temperature increases by t°C, the increase in length of the rod is

Δl = Lαt

The corresponding longitudinal strain is

Δl/L = αt

If Y be the Young’s modulus of the material of the rod, the stress developed is given by 

Stress = Y x strain = Yαt