A brass wire of length 2 m and radius 1 mm at $27^{\circ} \mathrm{C}$ is held taut between two rigid supports. Initially it was cooled to a temperature of $-43^{\circ} \mathrm{C}$ 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 1.4 T , is ______ $^{\circ} \mathrm{C}$

JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Heat & Thermodynamics

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 1.4 T , is ______

^{\circ} C

(A)-86
(B)-71✓ Correct
(C)-65
(D)-80

Answer: (B)

Solution

A wire clamped between rigid supports develops a thermal tension

T = α Y A Δ T

on cooling, where

Δ T

is measured from the stress-free temperature

2 7^{\circ}

C. Cooling to

- 4 3^{\circ}

C gives

T = α Y A [27 - (- 43)] = α Y A (70)

. For a tension

1.4 T

1.4 T = α Y A (27 - θ)

, so

1.4 = \frac{27 - θ}{70}

, giving

27 - θ = 98

. The wire must be cooled to

- 7 1^{\circ}

JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Single correct option

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