Correct Answer  Option 4 :
\(\frac{2}{5}~M{{r}^{2}}\)
CONCEPT:

Moment of Inertia: It is a quantity that expresses a body's tendency to resist angular acceleration, it is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation, is called the moment of Inertia.
 The moment of inertia is simply the mass times the square of the perpendicular distance of central to the axis of rotation.
I = m × r2
where I is the Moment of Inertia, m is point mass, r is the perpendicular distance from the axis of rotation.
The moment of inertia of different bodies is given in the below table:
Shape 
Axis of rotation 
Moment of inertia 
Ring 
axis passing through the center perpendicular to the plane of the ring 
\(I = mr^2\) 
Ring 
axis passing through the diameter of ring 
\(I = {1 \over 2}mr^2\) 
Solid Cylinder 
axis passing through the center perpendicular to the plane of the ring 
\(I = {1 \over 2}mr^2\) 
Solid sphere 
through center 
\(I = {2 \over 5}mr^2\) 
Hollow sphere 
through center 
\(I = {2 \over 3}mr^2\) 
Rod 
through midpoint perpendicular to the rod 
\(I = {1 \over 12}ml^2\) 
EXPLANATION:
From the above table, it is clear that the moment of inertia of a solid sphere of mass 'm' and radius 'R' about an axis passing through the center is:
\(I = {2 \over 5}mr^2\).
 So the correct answer is option 4.