STATEMENT-1 `:` When two isolated charged metal spheres are touched with each other potential energy of system may decrease.
and
STATEMENT-2 `:` There may be transfer of charge from one to other after touching.

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 both statements regarding the potential energy of two isolated charged metal spheres when they touch each other.

### Step-by-Step Solution:

1. **Understanding the Initial Setup**:
- Let's denote the charges on the two spheres as \( Q_1 \) and \( Q_2 \).
- The initial potential energy \( U_i \) of the system when the spheres are at a distance \( R \) apart is given by the formula:
\[ U_i = k \frac{Q_1 Q_2}{R} \]
where \( k \) is Coulomb's constant.

2. **Touching the Spheres**:
- When the two charged spheres are touched, they allow charge to redistribute between them. This process is known as charge sharing.
- After touching, the charges will redistribute until both spheres reach the same electric potential.

3. **Final Charges After Touching**:
- Let’s assume after touching, the charges on the spheres become \( Q_1' \) and \( Q_2' \).
- The total charge before touching is conserved, so:
\[ Q_1' + Q_2' = Q_1 + Q_2 \]
- Since they are conductors and will reach the same potential, we have:
\[ \frac{Q_1'}{C_1} = \frac{Q_2'}{C_2} \]
where \( C_1 \) and \( C_2 \) are the capacitances of the respective spheres.

4. **Calculating Final Potential Energy**:
- The final potential energy \( U_f \) after the charges have redistributed can be expressed as:
\[ U_f = k \frac{Q_1' Q_2'}{R} \]
- Depending on the values of \( Q_1 \) and \( Q_2 \), it is possible that \( U_f < U_i \).

5. **Conclusion on Potential Energy**:
- If the charges redistribute such that the product \( Q_1' Q_2' \) is less than \( Q_1 Q_2 \), then the potential energy of the system decreases after the spheres are touched.
- Therefore, Statement 1 is true: "When two isolated charged metal spheres are touched with each other, the potential energy of the system may decrease."

6. **Analyzing Statement 2**:
- Statement 2 states: "There may be transfer of charge from one to the other after touching."
- This is also true because touching the spheres allows charge to flow between them until they reach the same potential.

7. **Final Assessment**:
- Both statements are true, and Statement 2 provides a correct explanation for Statement 1.
- Therefore, the correct conclusion is that both statements are true, and Statement 2 is the correct explanation for Statement 1.

### Final Answer:
Both statements are true, and Statement 2 is the correct explanation for Statement 1.