Final answer:
The percentage change in mass density when a metal wire's temperature increases from 0°C to 10°C and its length increases by 0.02% is closest to 0.06%, which corresponds to option A.
Step-by-step explanation:
When a metal wire is heated and its temperature increases, it expands in length. This thermal expansion results in the wire having a greater volume but the same mass, which causes its mass density to decrease. The change in mass density (ρ) can be calculated using the formula for volume expansion: ρ'=ρ/(1+3αΔT), where α is the linear expansion coefficient and ΔT is the change in temperature.
However, since the change in temperature is small, the volume change is approximately equal to three times the linear change (as volume expansion coefficient ≈ 3× linear expansion coefficient for small temperature changes).
If the length of the wire increased by 0.02% for a 10°C increase in temperature, the volume would increase by approximately 0.06%. Given that mass density is inversely proportional to volume (if mass remains constant), the mass density would decrease by approximately the same percentage.
Consequently, the mass density decreases by approximately 0.06%, making the answer closest to option A (0.06%).