Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one.
Reason R: Capacitance of metallic spheres depend on the radii of spheres.
In the light of the above statements, choose the correct answer from the options given below.

Assertion A: Two metallic spheres are charged to the same potential. One is hollow and another is solid, both with the same radii. The solid sphere will have lower charge than the hollow one.

Reason R: Capacitance of metallic spheres depends on the radii of the spheres.

Analysis of Assertion A:

For a conducting sphere (whether solid or hollow), charge resides entirely on the outer surface. The potential of a sphere of radius $$R$$ carrying charge $$Q$$ is:

$$V = \frac{1}{4\pi\epsilon_0} \cdot \frac{Q}{R}$$

The capacitance is $$C = 4\pi\epsilon_0 R$$, which depends only on the radius $$R$$.

Since both spheres have the same radius $$R$$ and are charged to the same potential $$V$$:

$$Q = CV = 4\pi\epsilon_0 R \cdot V$$

Both spheres carry the same charge. Therefore, the assertion that the solid sphere has lower charge is false.

Analysis of Reason R:

The capacitance of a metallic sphere is $$C = 4\pi\epsilon_0 R$$, which indeed depends only on the radius. This statement is true.

Conclusion: A is false but R is true.

The answer is Option A: A is false but R is true.