Which of the following statements are correct?
(A) The electrostatic repulsive force between the protons can be greater than the nuclear force to bind the nucleons together inside a nucleus.
(B) The repulsive electrostatic force between protons in smaller nuclei is much smaller than the nuclear force between nucleons inside a nucleus.
(C) The gravitational force between nucleons is much smaller than the nuclear force between the nucleons inside a nucleus.
(D) The binding energy per nucleon between nucleons is almost constant because the nuclear force is a long range force.

Choose the correct answer from the options given below:

The correct answer is (B) and (C) only.

Let us analyze each of the statements step-by-step to understand the behavior of forces inside a nucleus:

Statement (A): "The electrostatic repulsive force between the protons can be greater than the nuclear force to bind the nucleons together inside a nucleus."
The strong nuclear force is the strongest known fundamental force in nature, acting at very short ranges of about 1 to 2 femtometers (fm). Inside a stable nucleus, this attractive nuclear force is approximately 100 times stronger than the repulsive electrostatic force acting between the positively charged protons. If the electrostatic repulsion were greater than the strong nuclear force, the nucleus would become unstable and immediately fly apart. Therefore, statement (A) is incorrect.

Statement (B): "The repulsive electrostatic force between protons in smaller nuclei is much smaller than the nuclear force between nucleons inside a nucleus."
In smaller nuclei, because the number of protons is low, the cumulative electrostatic repulsive force is relatively weak. Meanwhile, the nucleons are packed closely together within the range of the strong nuclear force. Consequently, the attractive nuclear force is vastly stronger than the repulsive electrostatic force, making statement (B) correct.

Statement (C): "The gravitational force between nucleons is much smaller than the nuclear force between the nucleons inside a nucleus."
The gravitational force is the weakest of the four fundamental forces and is directly proportional to the masses of the interacting particles. Because the masses of nucleons (protons and neutrons) are extremely small (on the order of 10^-27 kg), the gravitational attraction between them is virtually negligible. The ratio of the gravitational force to the strong nuclear force between two nucleons is of the order of:
$$\frac{F_g}{F_n}\approx {10}^{-38}$$
Since the gravitational force is indeed much smaller than the nuclear force, statement (C) is correct.

Statement (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 indeed nearly constant (around 8 MeV) for nuclei with a mass number:
$A$
between 30 and 170. However, this constancy is a direct consequence of the short-range nature of the nuclear force, which exhibits the property of saturation. A nucleon only interacts with its immediate neighboring nucleons, rather than with all nucleons in the nucleus. Because the nuclear force is a short-range force (not a long-range force), statement (D) is incorrect.

Thus, only statements (B) and (C) are correct.