JEE MainPhysicsModerateHeat

If the length of steel rod is 5cm longer than copper rod at all
temperatures. ( $\alpha$ for copper $= 1.7 \times 10^{- 5}ºC^{- 1}$ and
$\alpha$ for steel $\left. \ = 1.1 \times 10^{- 5}C^{- 1} \right)$

Show answer and solution

\mathcal{l}_{1}\left( 1 + \alpha_{1}\Delta T \right) - \mathcal{l}_{2}\left( 1 + \alpha_{2}\Delta T \right) = \mathcal{l}_{1} - \mathcal{l}_{2}

\mathcal{l}_{1}\alpha_{1}\Delta T = \mathcal{l}_{2}\alpha_{2}\Delta T

\mathcal{l}_{1}\alpha_{1} = \mathcal{l}_{2}\alpha_{2}

\Rightarrow \mathcal{l}_{1} \times 1.7 = \mathcal{l}_{2} \times 1.1

17\mathcal{l}_{1} = 11\mathcal{l}_{2}

\left( \mathcal{l}_{2} - \mathcal{l}_{1} = 5 \right)

\Rightarrow 17\mathcal{l}_{2} - 11\mathcal{l}_{2} = 5 \times 17

6\mathcal{l}_{2} = 85

\Rightarrow \mathcal{l}_{2} = \frac{85}{6} = 14.17cm

\mathcal{l}_{1} = 9.17cm

Source: Grass-G / P-08 Physics paper 23 October.docx

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