Question:easy

A copper rod and an iron rod of the same length have their temperature raised by the same amount. If the coefficient of linear expansion of copper is greater than that of iron, then

Show Hint

Remember that thermal expansion depends on the material's coefficient of linear expansion, and this property can vary significantly between different materials.
Updated On: Jun 3, 2026
  • Copper expands more than iron
  • Iron expands more than copper
  • Both expand by the same amount
  • Expansion depends on their masses
Show Solution

The Correct Option is A

Solution and Explanation

Step 1: Recall thermal expansion.
When a rod is heated, it grows longer. The increase in length is \[ \Delta L = \alpha L_0 \Delta T \] where $\alpha$ is the coefficient of linear expansion, $L_0$ is the starting length, and $\Delta T$ is the temperature rise.

Step 2: Note what is shared.
Both rods start with the same length $L_0$ and are heated by the same $\Delta T$. So the only difference is the value of $\alpha$ for each metal.

Step 3: Write each expansion.
For copper, \[ \Delta L_{Cu} = \alpha_{Cu} L_0 \Delta T \] For iron, \[ \Delta L_{Fe} = \alpha_{Fe} L_0 \Delta T \]

Step 4: Compare using the given fact.
We are told copper has a larger coefficient, so $\alpha_{Cu} > \alpha_{Fe}$. Since the other parts are equal, the bigger $\alpha$ wins. \[ \Delta L_{Cu} > \Delta L_{Fe} \]

Step 5: Note mass does not matter.
The formula has no mass in it. Expansion depends on length, temperature change, and material, not on how heavy the rod is.

Step 6: State the answer.
Copper expands more than iron. \[ \boxed{\text{Copper expands more than iron}} \]
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