A: A free proton is stable but inside a nucleus , a proton gets converted into a neutron, position and neutrino `(p to n+e^(+)+v)`.
R: Inside a nucleus, neutron decay `(n to p + e^(-)+barv)` as well as proton decay are possible, since other nucleons can share energy nad momentum to conserve energy as well as momentum and both the decays are in dynamic equillibrium .

Answer

To analyze the given assertion and reason, we will break down the concepts involved in the decay of protons and neutrons within a nucleus.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that a free proton is stable, but when it is inside a nucleus, it can be converted into a neutron, a positron (e⁺), and a neutrino (ν).
- This process is known as beta-plus decay (β⁺ decay). In this decay, a proton is transformed into a neutron, releasing a positron and a neutrino.

2. **Stability of Free Protons**:
- A free proton (not bound in a nucleus) is stable and does not undergo decay. This is because there are no other nucleons (neutrons or protons) to interact with and facilitate the decay process.

3. **Nuclear Stability**:
- Inside a nucleus, the stability of nucleons depends on the ratio of neutrons (N) to protons (Z). If the ratio (N/Z) is too low, the nucleus may be unstable, leading to the conversion of protons into neutrons to achieve stability.
- This conversion helps balance the forces within the nucleus, as neutrons contribute to the strong nuclear force without adding to the repulsive electromagnetic force that protons experience.

4. **Understanding the Reason**:
- The reason states that both neutron decay (n → p + e⁻ + ν̅) and proton decay (p → n + e⁺ + ν) are possible inside a nucleus due to the sharing of energy and momentum among nucleons.
- This sharing allows the conservation of energy, momentum, and charge during these decay processes.

5. **Dynamic Equilibrium**:
- The term "dynamic equilibrium" refers to the balance between the processes of proton decay and neutron decay. In a stable nucleus, these processes can occur in such a way that the overall composition remains stable.
- If the N/Z ratio is too high, neutrons can decay into protons, and if it is too low, protons can decay into neutrons, maintaining stability.

6. **Conclusion**:
- Both the assertion and reason are correct. The assertion correctly describes the behavior of protons in a nucleus, and the reason explains the underlying principles of nuclear stability and decay processes.

### Final Answer:
- **Assertion (A)**: Correct
- **Reason (R)**: Correct