Which of the following properties of a long steel bar would alter if the bar were melted, recast into a cube and allowed to cool to its original temperature?

Analyze the question: The steel bar is melted and recast into a cube, then cooled to its original temperature. We need to find which property changes.

Concept: Properties fall into two groups:

• Intrinsic (material) properties depend only on the substance, not its shape. Examples are density, specific heat capacity, and resistivity.
• Extrinsic properties depend on the shape and size of the object. Examples are electrical resistance, which depends on length and cross-sectional area.

Checking each option:

• A. Density (written "sensity" in the question): Density = mass/volume. The mass and the material are the same, and at the same temperature the density is unchanged. No change.
• B. Volume: No steel is lost, and at the same temperature the volume is the same. No change.
• C. Specific heat capacity: This depends only on the type of material (steel). No change.
• D. Electrical resistance: R = ρL/A. The resistivity ρ stays the same, but a long thin bar has a large L and small A. A cube has a small L and large A. So the resistance changes greatly. This changes.

Answer: The shape change alters the length and cross-sectional area of the conductor, so the electrical resistance changes.

Tip: If an object is only reshaped (same material, same mass, same temperature), the intrinsic properties (density, specific heat capacity, resistivity) and the mass and volume stay the same. Anything that depends on length or area, such as resistance, will change.