JEE Main 2026 — Jan 24, Shift 1 — Physics solution

JEE Main2026Jan 24, Shift 1Physics

A brass wire of length 2 m and radius 1 mm at $2 7^{\circ} C$ is held taut between two rigid supports. Initially it was cooled to a temperature of $- 4 3^{\circ} C$ creating a tension T in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to 1.4T, is ____ $^{\circ} C$ .

A
$- 86$
B
$- 71$
C
$- 65$
D
$- 80$

Solution

A taut wire cooled by $Δ T$ develops tension $T = α Y A Δ T$ , where $α$ , $Y$ , and $A$ are fixed for the wire.

At $- 4 3^{\circ}$ C: $Δ T_{1} = 27 - (- 43) = 7 0^{\circ}$ C, giving tension $T \propto 70$ .

For tension $1.4 T$ : required $Δ T_{2} = 1.4 \times 70 = 9 8^{\circ}$ C.

$∴$ Final temperature $θ = 27 - 98 = - 7 1^{\circ}$ C.

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