Two rods of lengths l1 and l2 are made of materials whose coefficients of linear expansion are α1 and α2 respectively. If the difference between the two lengths is independent of temperature, then

Question

Two rods of lengths l1 and l2 are made of materials whose coefficients of linear expansion are α1 and α2 respectively. If the difference between the two lengths is independent of temperature, then (A) (l1/l2)=(α2/α1) (B) l12 α2=l22 α1 (C) (l1/l2)=(α1/α2) (D) α22 l1=α12 l2

Tardigrade Admin · Accepted Answer

l1'=l1(1+α1 Δ T) l2'=l2(1+α2 Δ T) Now, (l1'-l2')=(l1-l2)+(l1 α1-l2 α2) Δ T As (l1'-l2')=(l1-l2) ⇒ Coefficient of Δ T=0 or l1 α1=l2 α2 ⇒ (l1/l2)=(α2/α1)666666

Q. Two rods of lengths $l_{1}$ and $l_{2}$ are made of materials whose coefficients of linear expansion are $α_{1}$ and $α_{2}$ respectively. If the difference between the two lengths is independent of temperature, then

$\frac{l _{1}}{l _{2}} = \frac{α _{2}}{α _{1}}$

$l_{1}^{2} α_{2} = l_{2}^{2} α_{1}$

$\frac{l _{1}}{l _{2}} = \frac{α _{1}}{α _{2}}$

$α_{2}^{2} l_{1} = α_{1}^{2} l_{2}$

Q. Two rods of lengths l1​ and l2​ are made of materials whose coefficients of linear expansion are α1​ and α2​ respectively. If the difference between the two lengths is independent of temperature, then

l2​l1​​=α1​α2​​

l12​α2​=l22​α1​

l2​l1​​=α2​α1​​

α22​l1​=α12​l2​

l1′​=l1​(1+α1​ΔT) l2′​=l2​(1+α2​ΔT) Now, (l1′​−l2′​)=(l1​−l2​)+(l1​α1​−l2​α2​)ΔT As (l1′​−l2′​)=(l1​−l2​) ⇒ Coefficient of ΔT=0 or l1​α1​=l2​α2​ ⇒l2​l1​​=α1​α2​​666666

Q. Two rods of lengths $l_{1}$ and $l_{2}$ are made of materials whose coefficients of linear expansion are $α_{1}$ and $α_{2}$ respectively. If the difference between the two lengths is independent of temperature, then

$\frac{l _{1}}{l _{2}} = \frac{α _{2}}{α _{1}}$

$l_{1}^{2} α_{2} = l_{2}^{2} α_{1}$

$\frac{l _{1}}{l _{2}} = \frac{α _{1}}{α _{2}}$

$α_{2}^{2} l_{1} = α_{1}^{2} l_{2}$