Statement-1 `:` If a pendulum clock is taken to a mountain top, it gains time.
Statement-2 `:` The value of acceleration due to gravity is low at mountain top than at plen.

Options

A. Statement -1 is true, Statement-2, Statement -2 is correct explanation of statement-1.
B. Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanantion of Statement-1.
C. Statement-1 is correct, Statement-2 is false.
D. Statement-1 is false, Statement-2 is true.

Explanation

To solve the problem, we need to analyze both statements and understand their relationship through physics concepts.

### Step-by-Step Solution:

1. **Understanding Statement 1**:
- Statement 1 claims that a pendulum clock gains time when taken to a mountaintop.
- To analyze this, we need to consider the formula for the time period of a simple pendulum:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
- Here, \(T\) is the time period, \(L\) is the length of the pendulum, and \(g\) is the acceleration due to gravity.

2. **Effect of Altitude on Gravity**:
- When we take the pendulum clock to a mountaintop, the value of \(g\) (acceleration due to gravity) decreases because gravity is weaker at higher altitudes.
- Therefore, we can conclude that \(g\) at the mountaintop is less than \(g\) at sea level (or a plane).

3. **Analyzing the Time Period**:
- Since \(g\) decreases at the mountaintop, we can observe how this affects the time period \(T\):
- If \(g\) decreases, then \(\sqrt{\frac{L}{g}}\) increases, which means that \(T\) (the time period) increases.
- An increase in the time period means that the pendulum takes longer to complete one oscillation.

4. **Conclusion for Statement 1**:
- Since the time period \(T\) increases, the pendulum clock will gain time (i.e., it will run slower compared to a clock at sea level).
- Therefore, Statement 1 is true.

5. **Understanding Statement 2**:
- Statement 2 states that the value of acceleration due to gravity is lower at the mountaintop than at the plane.
- This is a known fact in physics: as altitude increases, the value of \(g\) decreases.
- Thus, Statement 2 is also true.

6. **Relationship Between the Statements**:
- Statement 2 provides a correct explanation for Statement 1. The decrease in \(g\) at the mountaintop leads to an increase in the time period of the pendulum, causing the clock to gain time.

7. **Final Conclusion**:
- Both statements are true, and Statement 2 is the correct explanation for Statement 1.

### Answer:
- Statement 1 is true.
- Statement 2 is true.
- Statement 2 is the correct explanation of Statement 1.
- Therefore, the correct answer is option A.