Nuclear Force

Nuclear force is the fundamental force that binds nucleons (protons and neutrons) together in an atomic nucleus. It is a strong force, effective only over very short distances (on the order of femtometers), and is independent of the charges of the particles involved (i.e., charge independent).

Step 1: Understanding the Concept:
This question probes the properties of the nuclear force (strong force) that holds the nucleus together, comparing it with other fundamental forces and relating it to nuclear stability and binding energy.

Step 2: Detailed Explanation:
(A) The electrostatic repulsive force between the protons can be greater than the nuclear force to bind the nucleons together inside a nucleus.
If the electrostatic repulsion were greater than the attractive nuclear force, the nucleus would fly apart. This statement describes the condition for instability in very large, proton-rich nuclei, leading to fission or decay. It is not a general condition for all nuclei. However, the statement implies this can happen, which is true for unstable heavy nuclei. Let's hold this. For a stable nucleus, the nuclear force must be stronger. The statement is ambiguously worded. Let's re-evaluate. The question asks for correct statements in general. For stable nuclei, this is false. For unstable ones, it is true. Let's see other options. (B) The repulsive electrostatic force between protons in smaller nuclei is much smaller than the nuclear force between nucleons inside a nucleus.
The strong nuclear force is the strongest force in nature over short distances (within the nucleus). In small, stable nuclei (like Helium or Carbon), the attractive nuclear force overwhelmingly dominates the electrostatic repulsion between the few protons present. This is why these nuclei are very stable. This statement is correct.
(C) The gravitational force between nucleons is much smaller than the nuclear force between the nucleons inside a nucleus.
The gravitational force is by far the weakest of the four fundamental forces. At the nuclear scale, the gravitational attraction between nucleons is completely negligible compared to both the strong nuclear force and the electrostatic force. For instance, the strong force is about times stronger than gravity. This statement is correct.
(D) The binding energy per nucleon between nucleons is almost constant because the nuclear force is a long range force.
The binding energy per nucleon is almost constant for most nuclei (saturation property), but this is precisely because the nuclear force is a short-range force. A nucleon only interacts with its immediate neighbours. If the force were long-range, every nucleon would interact with every other nucleon, and the binding energy per nucleon would keep increasing with the mass number A. Thus, the reason given is incorrect. This statement is incorrect.
Re-evaluating (A): Given that (B) and (C) are definitively correct and (D) is definitively incorrect, let's look at the options. Option (2) contains (B) and (C). This suggests that statement (A) should be considered incorrect in the general context. For a nucleus to exist, even transiently, the nuclear force must be dominant. The electrostatic repulsion becoming greater is the cause of its disintegration. So, in the context of a bound system, (A) is false.

Step 3: Final Answer:
Statements (B) and (C) are correct descriptions of the forces within a nucleus. Statement (D) provides an incorrect reason for a correct observation. Statement (A) describes a condition for nuclear instability, not a general property of bound nuclei. Thus, (B) and (C) are the correct statements.