Q136 / 160 · AP EAMCET 2023 (17 May Shift 2) · Physics

A steel tape of $300 \mathrm{~cm}$ length is graduated at $27^{\circ} \mathrm{C}$. The length of a steel rod measured using the tape is found to be $110 \mathrm{~cm}$ at $50^{\circ} \mathrm{C}$. The actual length of steel rod at 50 ${ }^{\circ} \mathrm{C}$ is $\left(\alpha_{\text {steel }}=1.2 \times 10^{-5} \mathrm{~K}^{-1}\right)$

  • Correct answer
    A
    $110.03 \mathrm{~cm}$
  • B
    $110.10 \mathrm{~cm}$
  • C
    $110.07 \mathrm{~cm}$
  • D
    $110.62 \mathrm{~cm}$

Solution

Let $L^{\prime}$ be the length of steel rod. $\begin{aligned} & \mathrm{L}^{\prime}=\mathrm{L}+\mathrm{L} \alpha \Delta \mathrm{T} \\ & =300+300 \times 1.2 \times 10^{-5} \times(50-27) \\ & =300+0.0828=300.0828 \mathrm{~m}\end{aligned}$ The actual length of steel rod at $50^{\circ} \mathrm{C}$ is $\mathrm{L}_2=\frac{300.0828}{300} \times 110=110.03 \mathrm{~cm}$

Hence, the correct answer is option: 'A'.

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