Introduction:
In this question, we are given two spheres, S₁ and S₂, with different polarizations, Pok and Po respectively. We need to determine the correct statements regarding the surface bound charge density on these spheres.

Surface bound charge density:
Surface bound charge density refers to the charge distribution on the surface of an object. It arises due to the alignment of charges within the material of the object.

Statement 1: Surface bound charge density is non-uniform on S₁
Explanation:
The polarization P of a material is defined as the dipole moment per unit volume. Mathematically, P = Δp/ΔV, where Δp is the dipole moment and ΔV is the volume.

For sphere S₁, the polarization Pok is given. Since polarization is a vector quantity, it has both magnitude and direction. The polarization of S₁ is given as Pok = -k * P, where k is the unit vector in the z-direction.

The surface bound charge density σb on S₁ is related to the polarization by the equation σb = -P · n, where n is the unit vector normal to the surface. In this case, n is the unit vector radially outward from the center, which is f.

Since the polarization Pok is in the opposite direction of k, and k is in the z-direction, the surface bound charge density σb on S₁ will be non-uniform. This is because the dot product of Pok and f will vary across the surface of the sphere, resulting in a non-uniform charge distribution.

Therefore, the statement "Surface bound charge density is non-uniform on S₁" is correct.

Statement 2: Surface bound charge density is uniform on S₂
Explanation:
For sphere S₂, the polarization Po is given. The polarization Po is not given in terms of a specific direction, so we can assume it to be in any direction.

Since the polarization Po is not specified to be in the z-direction or any other specific direction, the surface bound charge density σb on S₂ will be uniform. This is because the dot product of Po and f will be constant across the surface of the sphere, resulting in a uniform charge distribution.

Therefore, the statement "Surface bound charge density is uniform on S₂" is correct.

Summary:
Based on the given information, we can conclude that:
- The surface bound charge density is non-uniform on sphere S₁ due to the given polarization Pok.
- The surface bound charge density is uniform on sphere S₂ as the polarization Po is not specified in terms of a specific direction.