A brass wire of length 2 m and radius 1 mm at 27°C is held taut between two rigid supports. Initially it was cooled to a temperature of −43°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 ___

A brass wire of length 2 m and radius 1 mm at 27°C is held taut between two rigid supports

Q. A brass wire of length 2 m and radius 1 mm at 27°C is held taut between two rigid supports. Initially it was cooled to a temperature of −43°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 ____ °C.

(A) −71

(B) −80

(D) −86

Correct Answer: −71

Explanation

For a wire held between rigid supports, thermal stress is directly proportional to the change in temperature.

Initial temperature drop:

\[ \Delta T_1 = 27 - ( -43 ) = 70^\circ\text{C} \]

This temperature change produces tension T in the wire.

To increase the tension to \(1.4T\), the temperature change must be:

\[ \Delta T_2 = 1.4 \times \Delta T_1 = 1.4 \times 70 = 98^\circ\text{C} \]

Let the final temperature be \( \theta \).

\[ 27 - \theta = 98 \]

\[ \theta = 27 - 98 = -71^\circ\text{C} \]

Therefore, the required temperature is −71°C.

Explanation

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