Given below are two statements: One is labeled as Assertion A and the other is labeled 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 light of the above statements, choose the correct answer from the options given below.

Solution

Physics sir · 4 steps

Charge on a conductor sits only on its outer surface, so solid or hollow makes no difference at all.

1. Where charge sits. In a conductor at equilibrium, the field inside is zero, so all the charge moves to the outer surface. The inside of a solid sphere carries no charge, just like the empty inside of a hollow one.
2. Capacitance of sphere. For an isolated metal sphere, V = Q/(4πε₀ R), so its capacitance depends only on the radius.

   C = 4πε₀ R ⇒ Q = 4πε₀ R V

3. Check each statement. Same R and same V give the same Q for both spheres. So the solid sphere does not hold less charge, and A is false. R is true because C depends on the radius.
4. So. A is false but R is true, which is option (c).

The idea to keep. For any conductor, only the outer surface matters. Two metal spheres of the same radius have the same capacitance, 4πε₀ R, whether they are solid or hollow.

Answer from the NTA final answer key. Solution by PrepWiser.