Two rods A and B of identical dimensions are at temperature 30^ C . If A is heated upto 180^ C and B upto T^ C, then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4: 3

Correct answer: A. 230^ C Change in length in both rods are same i.e. Δ _ 1 =Δ _ 2 α_ 1 Δ θ_ 1 = α_ 2 Δ θ_ 2 array l α_ 1 α_ 2 = Δ θ_ 2 Δ θ_ 1 [ α_ 1 α_ 2 =(4)/(3)] (4)/(3)=(θ-30)/(180-30) array θ=230^ C

JEE Main 201911 JanuaryEvening Shift

Exam: JEE Main
Year: 2019
Date: 11 January
Shift: Evening Shift
Subject: Physics
Chapter: Thermal Properties of Matter

JEE Main 2019 · 11 January · Evening Shift · Physics · Thermal Properties of Matter

Two rods A and B of identical dimensions are at temperature 30^ C ....

Two rods

A

and

B

of identical dimensions are at temperature

30^{\circ} \mathrm{C}

. If

\mathrm{A}

is heated upto

180^{\circ} \mathrm{C}

and

\mathrm{B}

upto

\mathrm{T}^{\circ} \mathrm{C},

then the new lengths are the same. If the ratio of the coefficients of linear expansion of

\mathrm{A}

and

\mathrm{B}

4: 3,

then the value of

T

Options

A $230^{\circ} \mathrm{C}$
B $270^{\circ} \mathrm{C}$
C $200^{\circ} \mathrm{C}$
D $250^{\circ} \mathrm{C}$

Correct answer

A. $230^{\circ} \mathrm{C}$

Step-by-step solution

Change in length in both rods are same i.e.

\Delta \ell_{1}=\Delta \ell_{2}

\ell \alpha_{1} \Delta \theta_{1}=\ell \alpha_{2} \Delta \theta_{2}

\begin{array}{l} \frac{\alpha_{1}}{\alpha_{2}}=\frac{\Delta \theta_{2}}{\Delta \theta_{1}} \quad\left[\because \frac{\alpha_{1}}{\alpha_{2}}=\frac{4}{3}\right] \\ \frac{4}{3}=\frac{\theta-30}{180-30} \end{array}

\theta=230^{\circ} \mathrm{C}

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