In a zero gravity environment, the buoyant forces acting on the water and mercury inside the hollow glass spheres will be equal to the gravitational forces acting on them.

Option 1 states that both water and mercury will float freely inside the sphere. This is the correct answer. Since both liquids fill about one-tenth of the volume of the sphere, they have equal buoyant forces and will not settle or form layers on the glass. Instead, they will remain suspended and float freely within the sphere.

Option 2 suggests that only water will form a layer on the glass while mercury floats. This option is incorrect because in a zero gravity environment, there are no gravitational forces pulling the liquids downwards, allowing them to freely float.

Option 3 states that only mercury will form a layer on the glass while water floats. This option is also incorrect because both liquids will experience the same buoyant force, preventing them from settling or forming layers.

Option 4 suggests that both water and mercury will form a layer on the glass. However, in a zero gravity environment, the liquids will not settle on the glass but instead float freely.

Therefore, the correct answer is Option 1.