A metal rod of Young's modulus Y and coefficient of thermal expansion α is held at its two ends such that its length remains invariant. If its temperature is raised by t°C, the linear stress developed in its is :

Question

A metal rod of Young's modulus Y and coefficient of thermal expansion α is held at its two ends such that its length remains invariant. If its temperature is raised by t°C, the linear stress developed in its is : (A) (Y/α t) (B) Yα t (C) (1/(Yα t)) (D) (α t/Y)

Tardigrade Admin · Accepted Answer

(Δℓ/ℓ) = α.Δ T and Y = (F/ A/Δℓ/ℓ) So, F = AYα t Thermal stress ((F/A)) = Yα t.

Q. A metal rod of Young's modulus Y and coefficient of thermal expansion $α$ is held at its two ends such that its length remains invariant. If its temperature is raised by t $^{\circ}$ C, the linear stress developed in its is :

$\frac{Y}{α t}$

$Y α t$

$\frac{1}{( Y α t )}$

$\frac{α t}{Y}$

$\frac{Δ ℓ}{ℓ} = α .Δ T$
and $Y = \frac{F / A}{Δ ℓ / ℓ}$
So, $F = A Y α t$
Thermal stress $(\frac{F}{A}) = Y α t .$

Q. A metal rod of Young's modulus Y and coefficient of thermal expansion α is held at its two ends such that its length remains invariant. If its temperature is raised by t∘C, the linear stress developed in its is :

αtY​

Yαt

(Yαt)1​

Yαt​