STATEMENT-1`:` If potential energy of a dipole in stable equilibrium position is zero, its potential energy is unstable equilibrium position will be 2pE, where p and E represent the dipole moment and electric field respectively
and
STATEMENT-2 `:` The potential energy of a dipole is minimum in stable equilibruim position and maximum in unstable equilibrium position.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False , Statement-2 is True

Answer

To solve the problem, we need to analyze the two statements provided regarding the potential energy of a dipole in electric fields.

### Step-by-Step Solution:

1. **Understanding Stable and Unstable Equilibrium**:
- In a stable equilibrium position, the dipole aligns with the electric field. The potential energy (U) in this position is given by:
\[ U = -\vec{p} \cdot \vec{E} = -pE \cos(0) = -pE \]
- In an unstable equilibrium position, the dipole is oriented opposite to the electric field. The potential energy in this position is:
\[ U = -\vec{p} \cdot \vec{E} = -pE \cos(180^\circ) = pE \]

2. **Calculating the Difference in Potential Energy**:
- If we assume that the potential energy in stable equilibrium is zero (U_stable = 0), then we can express the potential energy in unstable equilibrium as:
\[ U_{unstable} = U_{unstable} - U_{stable} = pE - (-pE) = pE + pE = 2pE \]
- Thus, if the potential energy in stable equilibrium is zero, the potential energy in unstable equilibrium will indeed be \(2pE\).

3. **Analyzing Statement 1**:
- Statement 1 claims that if the potential energy of a dipole in stable equilibrium is zero, then its potential energy in unstable equilibrium will be \(2pE\). This statement is **true** based on our calculations.

4. **Analyzing Statement 2**:
- Statement 2 states that the potential energy of a dipole is minimum in stable equilibrium and maximum in unstable equilibrium.
- From our calculations, we see that in stable equilibrium, the potential energy is \(-pE\) (which is indeed a minimum), and in unstable equilibrium, it is \(pE\) (which is indeed a maximum). Therefore, this statement is also **true**.

5. **Determining the Relationship Between the Statements**:
- While both statements are true, Statement 2 does not provide a correct explanation for Statement 1. Statement 1 is a specific condition regarding potential energies, while Statement 2 is a general observation about the nature of potential energy in dipoles.

### Conclusion:
- **Statement 1 is true.**
- **Statement 2 is true.**
- **Statement 2 does not correctly explain Statement 1.**

Thus, the final answer is that both statements are true, but Statement 2 is not a correct explanation for Statement 1.