Question

A rod of length 1 m expands by 1 mm when temperature increases by 100°C. Coefficient of linear expansion is:

• A. $10^{-5}$
• B. $10^{-4}$
• C. $10^{-3}$
• D. $10^{-6}$

Hint:

Always ensure your units are consistent before plugging them into the formula. Converting $1$ mm to $10^{-3}$ m is the crucial first step to avoid order-of-magnitude errors.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Thermal expansion is the increase in the volume or dimensions of a material due to an increase in its temperature.
Step 2: Key Formula or Approach:
Linear expansion formula: \[ \Delta L = L_{0} \alpha \Delta T \]
Rearranging for \(\alpha\): \[ \alpha = \frac{\Delta L}{L_{0} \Delta T} \]
Step 3: Detailed Explanation:
Original length \(L_{0} = 1\) m.
Expansion \(\Delta L = 1\) mm = \(10^{-3}\) m.
Temperature rise \(\Delta T = 100^\circ\)C = \(10^{2}\) K.
\[ \alpha = \frac{10^{-3}}{1 \times 10^{2}} = 10^{-5} /^\circ\text{C} \]
Step 4: Final Answer:
The coefficient is \(10^{-5}\).