M.I. of solid sphere, is A. $$\frac{2}{3}{\text{M}}{{\text{r}}^2}$$ B. $$\frac{2}{5}{\text{M}}{{\text{r}}^2}$$ C. $${\text{M}}{{\text{r}}^2}$$ D. $$\frac{1}{2}{\text{M}}{{\text{r}}^2}$$

The moment of inertia of a solid sphere about an axis through its center of mass is $\frac{2}{5}{\text{M}}{{\text{r}}^2}$. This is because the mass of a solid sphere is distributed evenly throughout its volume, and the moment of inertia of a point mass about an axis is $mr^2$. Therefore, the moment of inertia of a solid sphere about an axis through its center of mass is the sum of the moments of inertia of all the point masses in the sphere, which is $\frac{2}{5}{\text{M}}{{\text{r}}^2}$.

The other options are incorrect because they do not take into account the fact that the mass of a solid sphere is distributed evenly throughout its volume. Option A is the moment of inertia of a rod about an axis through its center of mass, option B is the moment of inertia of a thin plate about an axis through its center of mass, and option C is the moment of inertia of a point mass about an axis.