Question:
A rod of length 1 m expands by 1 mm when temperature increases by 100°C. Coefficient of linear expansion is:
A rod of length 1 m expands by 1 mm when temperature increases by 100°C. Coefficient of linear expansion is:
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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.
Updated On: Jun 3, 2026
- $10^{-5}$
- $10^{-4}$
- $10^{-3}$
- $10^{-6}$
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The Correct Option is A
Solution and Explanation
Concept:
Thermal expansion is the tendency of matter to change its shape, area, and volume in response to a change in temperature. For solid materials, the change in length ($\Delta L$) is directly proportional to the original length ($L_0$) and the change in temperature ($\Delta T$).
Step 1: Identify the given values.
• Original length ($L_0$) = 1 m
• Change in length ($\Delta L$) = 1 mm = $10^{-3}$ m
• Change in temperature ($\Delta T$) = 100°C
Step 2: Apply the formula for linear expansion.
The coefficient of linear expansion ($\alpha$) is given by: \[ \Delta L = L_0 \alpha \Delta T \] Rearranging for $\alpha$: \[ \alpha = \frac{\Delta L}{L_0 \Delta T} \]
Step 3: Calculate the final value.
Substituting the values: \[ \alpha = \frac{10^{-3}}{1 \times 100} \] \[ \alpha = \frac{10^{-3}}{10^2} \] \[ \alpha = 10^{-5} / \text{°C} \]
Step 1: Identify the given values.
• Original length ($L_0$) = 1 m
• Change in length ($\Delta L$) = 1 mm = $10^{-3}$ m
• Change in temperature ($\Delta T$) = 100°C
Step 2: Apply the formula for linear expansion.
The coefficient of linear expansion ($\alpha$) is given by: \[ \Delta L = L_0 \alpha \Delta T \] Rearranging for $\alpha$: \[ \alpha = \frac{\Delta L}{L_0 \Delta T} \]
Step 3: Calculate the final value.
Substituting the values: \[ \alpha = \frac{10^{-3}}{1 \times 100} \] \[ \alpha = \frac{10^{-3}}{10^2} \] \[ \alpha = 10^{-5} / \text{°C} \]
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