Final answer:
In Physics, the change in the moment of inertia (ΔI) of a solid body due to a small temperature change (ΔT) is given as ΔI = 2αIΔT, with α representing the coefficient of linear expansion. This is based on the concept of thermal expansion, which describes how dimensions of an object change with temperature. The correct answer is option C.
Step-by-step explanation:
The question concerns the concept of thermal expansion in Physics and specifically relates to the change in the moment of inertia (I) of a solid body as a result of a small temperature change (ΔT). When the temperature of an object increases, its linear dimensions change by an amount proportional to the original dimensions and the temperature change. This effect is quantified by the coefficient of linear expansion (α).
For a solid body undergoing thermal expansion, the change in any linear dimension, such as length (L), can be expressed as ΔL = αLΔT. In two dimensions, the change in area (ΔA) is given by ΔA = 2αAΔT. By extension, we expect the change in moment of inertia to be linked to the change in dimensions due to thermal expansion. Therefore, considering the dimensional dependence of the moment of inertia, for a solid body that is uniform and symmetrical, the change in moment of inertia (ΔI) due to thermal expansion can be approximated to be proportional to the change in area. Hence, the correct answer to the question would be ΔI = 2αIΔT, corresponding to option C. For more complex shapes, the calculation might be more involved, but for small temperature changes and assuming a uniform material, this approximation holds true.