Q 11-10-051JEE MainJEE Main 2026 (24 Jan, Shift 1)Medium
A brass wire of length 2 m and radius 1 mm at $27^\circ\text{C}$ is held taut between two rigid supports. Initially it was cooled to a temperature of $-43^\circ\text{C}$ 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 ______ $^\circ\text{C}$.
Answer: (A) -71
Thermal tension in a wire held between rigid supports: $T = YA\alpha\,\Delta\theta$, so $T\propto\Delta\theta$ (drop below $27^\circ$C, where the wire is just taut).
Cooling to $-43^\circ$C: $\Delta\theta = 70^\circ$C gives $T$.
For $1.4T$: $\Delta\theta = 1.4\times70 = 98^\circ$C.
Required temperature $= 27 - 98 = -71^\circ$C.
Solution by Sreeraj P, M.Sc Physics