JEE Main 2026 — Apr 4, Shift 2 — Physics solution

JEE Main2026Apr 4, Shift 2Physics

The temperature of a metal strip having coefficient of linear expansion $α$ is increased from $T_{1}$ to $T_{2}$ resulting in increase of its length by $Δ L_{1}$ . The temperature is further increased from $T_{2}$ to $T_{3}$ such that the increase in its length is $Δ L_{2}$ .

Given $T_{3} + T_{1} = 2 T_{2}$ and $T_{2} - T_{1} = Δ T$ , the value of $Δ L_{2}$ is ________.

A
$Δ L_{1} [1 + 2 α^{2} (Δ T)^{2}]$
B
$Δ L_{1} [1 + α^{2} (Δ T)^{2}]$
C
$Δ L_{1} [1 + 2 α Δ T]$
D
$Δ L_{1} [1 + α Δ T]$

Solution

From the constraints, $T_{3} - T_{2} = T_{2} - T_{1} = Δ T$ (equal temperature increments in both stages).

Stage 1: $Δ L_{1} = L_{0} α Δ T$ , ending with length $L_{0} + Δ L_{1}$ .

Stage 2: using the new length as the reference,

$Δ L_{2} = (L_{0} + Δ L_{1}) α Δ T = L_{0} α Δ T + Δ L_{1} α Δ T = Δ L_{1} + Δ L_{1} α Δ T$ .

$∴ Δ L_{2} = Δ L_{1} (1 + α Δ T)$ .

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