Read the given statements and select the correct option.
Statement 1: A pendulum can vibrate in an artificial satellite.
Statement 2 : Inside the satellite acceleration due to gravity is zero.

Options

A. Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1.
B. Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1.
C. Statement 1 is true but statement 2 is false.
D. Statement 1 is false but statement 2 is true.

Explanation

To solve the question, we need to analyze both statements provided:

**Statement 1:** A pendulum can vibrate in an artificial satellite.
**Statement 2:** Inside the satellite, acceleration due to gravity is zero.

### Step-by-Step Solution:

1. **Understanding Statement 2:**
- Inside an artificial satellite, the satellite is in a state of free fall towards the Earth. This creates a condition known as "weightlessness" for objects inside the satellite.
- Although the gravitational force is still present, the acceleration due to gravity (g) is effectively zero for objects inside the satellite because they are in free fall along with the satellite.

**Conclusion for Statement 2:** This statement is **True**.

2. **Understanding Statement 1:**
- A pendulum relies on the force of gravity to oscillate. The formula for the time period (T) of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \(L\) is the length of the pendulum and \(g\) is the acceleration due to gravity.
- If we substitute \(g = 0\) (as per Statement 2), we find that:
\[ T = 2\pi \sqrt{\frac{L}{0}} \rightarrow T = \infty \]
- This implies that the pendulum does not oscillate at all because it cannot complete a swing back and forth without the force of gravity acting on it.

**Conclusion for Statement 1:** This statement is **False**.

3. **Final Evaluation:**
- Since Statement 1 is false and Statement 2 is true, the correct option is that Statement 1 is false and Statement 2 is true.

### Final Answer:
The correct option is **Option 4**: Statement 1 is false, Statement 2 is true.

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