Coefficient of linear expansion of brass and steel rods are α1 and α2. Lengths of brass and steel rods are l1 and l2 respectively. If (l2 - l1) is maintained same at all temperatures, which one of the following relations holds good ?

Question

Coefficient of linear expansion of brass and steel rods are α1 and α2. Lengths of brass and steel rods are l1 and l2 respectively. If (l2 - l1) is maintained same at all temperatures, which one of the following relations holds good ? (A) α1 l22 = α2 l12 (B) α12 l2 = α22 l1 (C) α1 l1 = α2 l2 (D) α1 l2 = α2 l1

Tardigrade Admin · Accepted Answer

Change in length for both rods should be same Δ ℓ1 = Δ ℓ2 ℓ1 α1 Δ T = ℓ2 α2 Δ T ℓ1 α1 = ℓ2 α2

Q. Coefficient of linear expansion of brass and steel rods are $α_{1}$ and $α_{2}$ . Lengths of brass and steel rods are $l_{1}$ and $l_{2}$ respectively. If $(l_{2} - l_{1})$ is maintained same at all temperatures, which one of the following relations holds good ?

$α_{1} l_{2}^{2} = α_{2} l_{1}^{2}$

$α_{1}^{2} l_{2} = α_{2}^{2} l_{1}$

$α_{1} l_{1} = α_{2} l_{2}$

$α_{1} l_{2} = α_{2} l_{1}$

Change in length for both rods should be same
$Δ ℓ_{1} = Δ ℓ_{2}$
$ℓ_{1} α_{1} Δ T = ℓ_{2} α_{2} Δ T$
$ℓ_{1} α_{1} = ℓ_{2} α_{2}$

Q. Coefficient of linear expansion of brass and steel rods are α1​ and α2​. Lengths of brass and steel rods are l1​ and l2​ respectively. If (l2​−l1​) is maintained same at all temperatures, which one of the following relations holds good ?

α1​l22​=α2​l12​

α12​l2​=α22​l1​

α1​l1​=α2​l2​

α1​l2​=α2​l1​