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MCQEasyJEE 2026Young's Modulus, Bulk & Rigidity Modulus

JEE Physics 2026 Question with Solution

A brass wire of length 2 m2 \, \text{m} and radius 1 mm1 \, \text{mm} at 27∘C27^\circ \text{C} is held taut between two rigid supports. Initially it was cooled to a temperature of −43∘C-43^\circ \text{C} creating a tension TT in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to 1.4T1.4T is _____∘C^\circ \text{C}.

  • A

    −71-71

  • B

    −65-65

  • C

    −80-80

  • D

    −86-86

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: A brass wire is fixed between rigid supports at 27∘C27^\circ \text{C}. When cooled to −43∘C-43^\circ \text{C}, the tension is TT. Find: the temperature at which the tension becomes 1.4T1.4T.

For a wire fixed between rigid supports, thermal stress is given by

σ=YαΔT\sigma = Y \alpha \Delta T

Hence, the tension is directly proportional to the temperature change.

So, for two conditions,

T2T1=ΔT2ΔT1\frac{T_2}{T_1} = \frac{\Delta T_2}{\Delta T_1}

Given that

T2=1.4T1T_2 = 1.4T_1

The initial temperature change is

ΔT1=27−(−43)=70∘C\Delta T_1 = 27 - (-43) = 70^\circ \text{C}

Therefore, the new temperature change is

ΔT2=1.4×70=98∘C\Delta T_2 = 1.4 \times 70 = 98^\circ \text{C}

Let the required final temperature be TfT_f. Then

27−Tf=9827 - T_f = 98

So,

Tf=27−98=−71∘CT_f = 27 - 98 = -71^\circ \text{C}

Therefore, the wire must be cooled to −71∘C-71^\circ \text{C}. The correct option is A.

Common mistakes

  • Using the absolute final temperature instead of the temperature change. Thermal stress depends on ΔT\Delta T, not directly on the final temperature. First calculate the cooling from 27∘C27^\circ \text{C}.

  • Taking ΔT1=−43−27\Delta T_1 = -43 - 27 and carrying the negative sign into the ratio. Here only the magnitude of cooling determines the increase in tension, so use 27−(−43)=70∘C27 - (-43) = 70^\circ \text{C}.

  • Assuming length or radius is needed in the calculation. Since the wire is fixed between rigid supports and the same wire is compared in both cases, the ratio of tensions depends only on the ratio of temperature changes.

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