Question

A metal rod of Young's moduls 'Y' and coefficient of linear expansion 'a' has its temeprature raised by 'Δ θ'. The linear stress to prevent the expansion of rod is ______.
(L and l is original length of rod and expansion respectively)

Options

• Y ∝ Δ θ

• `"Y"(l/"L")^2`

• `"Y" "L"/l`

• `("Y" prop)/(Delta theta)`

Answer 1

A metal rod of Young's moduls 'Y' and coefficient of linear expansion 'a' has its temeprature raised by 'Δ θ'. The linear stress to prevent the expansion of rod is Y ∝ Δ θ.

Explanation:

For thermal expansion

Δ L = L Δ θ

If rod is compress by Δ L, then

Δ L = `"FL"/"AY"`

`therefore "FL"/"AY" = "L" prop Delta theta`

`therefore "F"/"A" = "Y" prop Delta theta`