Q200 / 200 · AP EAMCET 2001 · Physics

A steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5} \mathrm{~m}$ at a certain temperature. The maximum temperature variation allowable during the ruling is (Coefficient of linear expansion of steel $=10 \times 10^{-6} \mathrm{~K}^{-1}$ )

  • A
    $2^{\circ} \mathrm{C}$
  • Correct answer
    B
    $5^{\circ} \mathrm{C}$
  • C
    $7^{\circ} \mathrm{C}$
  • D
    $10^{\circ} \mathrm{C}$

Solution

Change in length $\Delta L=5 \times 10^{-5} \mathrm{~m}$ Initial length $L=1 \mathrm{~m}$ $\alpha=10 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ $\therefore$ Change in temperature $\begin{aligned} \Delta t & =\frac{\Delta L}{\alpha L}=\frac{5 \times 10^{-5}}{10 \times 10^{-6} \times 1} \\ & =5^{\circ} \mathrm{C}\end{aligned}$

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

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