M.I. of solid sphere, is

Solution (By Examveda Team)

The moment of inertia (II) of a solid sphere can be calculated using the formula:

I=$$\frac{2}{5}{\text{M}}{{\text{r}}^2}$$

Where:
I is the moment of inertia.
M is the mass of the sphere.
r is the radius of the sphere.

In this formula, we can see that the moment of inertia depends on both the mass of the sphere (MM) and the square of its radius (r²). The factor $$\frac{2}{5}$$ is a constant that relates to the distribution of mass within a solid sphere. This formula is specific to solid spheres and is derived from the integration of infinitesimal mass elements over the entire volume of the sphere.

So, the moment of inertia for a solid sphere is $$\frac{2}{5}$$​ times the product of its mass and the square of its radius. This property is important in physics and engineering, especially when analyzing the rotational motion of objects.