A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion α / °C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by Δ T K. Young's modulus, Y, for this metal is :

Question

A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion α / °C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by Δ T K. Young's modulus, Y, for this metal is : (A) (F/2AαΔ T)  (B) (F/Aα (Δ T - 273))  (C) (F/Aα Δ T) (D) (2F/Aα Δ T)

Tardigrade Admin · Accepted Answer

Young's modulus y = ( textStress/ textStrain) =(F/A/(Δ ℓ/ℓ)) = (F/A(α Δ T))

$\frac{F}{2 A α Δ T}$

$\frac{F}{A α ( Δ T - 273 )}$

$\frac{F}{A α Δ T}$

$\frac{2 F}{A α Δ T}$

Young's modulus $y = \frac{Stress}{Strain}$
$= \frac{F / A}{( Δ ℓ / ℓ )}$
$= \frac{F}{A ( α Δ T )}$

2AαΔTF​

Aα(ΔT−273)F​

AαΔTF​

AαΔT2F​

Young's modulus y=StrainStress​ =(Δℓ/ℓ)F/A​ =A(αΔT)F​

$\frac{F}{2 A α Δ T}$

$\frac{F}{A α ( Δ T - 273 )}$

$\frac{F}{A α Δ T}$

$\frac{2 F}{A α Δ T}$

Young's modulus $y = \frac{Stress}{Strain}$
$= \frac{F / A}{( Δ ℓ / ℓ )}$
$= \frac{F}{A ( α Δ T )}$