Statement-1 : Time period of simple harmonic motion at moon greater than that on earth.
because
Statement-2: There is no atmosphere on moon.

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 and their relationship to each other.

### Step 1: Understand the Time Period of Simple Harmonic Motion (SHM)
The time period \( T \) of a simple pendulum, which is a classic example of SHM, is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.

### Step 2: Compare the Acceleration Due to Gravity on Earth and Moon
On Earth, the acceleration due to gravity \( g \) is approximately \( 9.8 \, \text{m/s}^2 \). On the Moon, the acceleration due to gravity \( g' \) is about \( \frac{g}{6} \) or approximately \( 1.63 \, \text{m/s}^2 \).

### Step 3: Analyze the Effect of Gravity on the Time Period
Since the time period \( T \) is inversely proportional to the square root of \( g \), we can see that:
- As \( g \) decreases (which it does on the Moon), the time period \( T \) increases.

This implies that the time period of a simple pendulum on the Moon is greater than that on Earth. Thus, **Statement 1** is true.

### Step 4: Evaluate the Reasoning Behind Statement 1
**Statement 2** claims that the reason for the longer time period on the Moon is due to the absence of an atmosphere. However, the absence of an atmosphere does not directly affect the time period of a pendulum. The time period is primarily affected by the gravitational acceleration \( g \), not the presence or absence of an atmosphere.

### Conclusion
- **Statement 1** is true: The time period of SHM on the Moon is greater than that on Earth.
- **Statement 2** is false as it does not provide a correct explanation for Statement 1.

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

### Final Answer
- **Statement 1**: True
- **Statement 2**: False (not a correct explanation)