A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by Δ T. The net change in its length is zero. Let l be the length of the rod, A its area of cross-section, Y its Young’s modulus, and α its coefficient of linear expansion. Then, F is equal to :

Question

A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by Δ T. The net change in its length is zero. Let l be the length of the rod, A its area of cross-section, Y its Young’s modulus, and α its coefficient of linear expansion. Then, F is equal to : (A) l2 Y α Δ T  (B) l A Y α Δ T  (C) A Y α Δ T  (D) (A Y/α Δ T )

Tardigrade Admin · Accepted Answer

Net change in length = 0 Thermal Exp. = l propto Δ t y = (F/A/Δ l / l) (Δ l/l) = (F/Ay) Δ l = (Fl/Ay) (Fl/Ay) = l propto Δ t F = Ay propto Δ t

$l^{2} Y α Δ T$

$l A Y α Δ T$

$A Y α Δ T$

$\frac{A Y}{α Δ T}$

Net change in length = 0
Thermal Exp. = $l \propto Δ t$
$y = \frac{F / A}{Δ l / l}$
$\frac{Δ l}{l} = \frac{F}{A y}$
$Δ l = \frac{Fl}{A y}$
$\frac{Fl}{A y} = l \propto Δ t$
$F = A y \propto Δ t$

l2YαΔT

lAYαΔT

AYαΔT

αΔTAY​

Net change in length = 0 Thermal Exp. = l∝Δt y=Δl/lF/A​ lΔl​=AyF​ Δl=AyFl​ AyFl​=l∝Δt F=Ay∝Δt

$l^{2} Y α Δ T$

$l A Y α Δ T$

$A Y α Δ T$

$\frac{A Y}{α Δ T}$

Net change in length = 0
Thermal Exp. = $l \propto Δ t$
$y = \frac{F / A}{Δ l / l}$
$\frac{Δ l}{l} = \frac{F}{A y}$
$Δ l = \frac{Fl}{A y}$
$\frac{Fl}{A y} = l \propto Δ t$
$F = A y \propto Δ t$