Question

The standard of length is maintained by a 1 meter long bar made up of a material having coefficient of linear expansion \( \alpha = 10^{-5}\,\text{°C}^{-1} \). If the length of the bar were to be preserved to an accuracy of 1 part per million, what would be the maximum allowed temperature variation?

• A. \( \pm 0.01^\circ C \)
• B. \( \pm 0.1^\circ C \)
• C. \( \pm 0.001^\circ C \)
• D. \( \pm 0.0001^\circ C \)
• E. \( \pm 1.0^\circ C \)

Hint:

Very small temperature changes can affect precision measurements due to thermal expansion.

Answer 1

The Correct Option is B

Concept:
\[ \frac{\Delta L}{L} = \alpha \Delta T \]

Step 1: Accuracy condition
\[ \frac{\Delta L}{L} = 10^{-6} \]

Step 2: Substitute
\[ 10^{-6} = 10^{-5} \Delta T \]

Step 3: Solve
\[ \Delta T = \frac{10^{-6}}{10^{-5}} = 0.1^\circ C \]

Step 4: Final answer
\[ \boxed{\pm 0.1^\circ C} \]