Q1: Consider the following statements :
A : An isotropic material is always homogeneous.
R : An isotropic material is one in which all the properties are the same in all the directions
at every point.
Of these statements :

ANS:B - Both A and R are true but R is not a correct explanation of A

Both statements are false.

No, Isotropic materials can be homogeneous, but they are not always this way.

An isotropic property means that the property behaves the same in all directions. Earth's gravity field is (mostly) isotropic. Its pull weakens, in the same way, the further away you get from it, no matter what direction you move away from it. It's not homogeneous, because it varies with the distance from its centre.

If you consider an ideal vacuum chamber, it would be both homogeneous and isotropic. It's homogeneous because it is uniformly devoid of any gas or matter. It's isotropic because its gas density is uniform in all directions.

Homogeneity implies isotropy, but not everything that is isotropic is homogeneous.

Isotropic Material - same physical property in all directions at a point.