Statement-1 : Time period of a simple pendulum remains unchanged if solid bob is replaced by hollow bob of same radius but lesser mass.
Statement-2 Time period of a simple pendulum depends on the mass but does not depend on the density.

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 time period of a simple pendulum.

### Step-by-Step Solution:

1. **Understanding the Time Period of a Simple Pendulum**:
The time period \( T \) of a simple pendulum 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. Importantly, the formula shows that the time period does not depend on the mass of the bob.

2. **Analyzing Statement 1**:
- Statement 1 claims that the time period remains unchanged if a solid bob is replaced by a hollow bob of the same radius but lesser mass.
- Since the radius (and thus the effective length \( L \)) remains the same and the acceleration due to gravity \( g \) does not change, the time period \( T \) will remain the same regardless of whether the bob is solid or hollow.
- Therefore, **Statement 1 is true**.

3. **Analyzing Statement 2**:
- Statement 2 claims that the time period of a simple pendulum depends on the mass but does not depend on the density.
- However, as established earlier, the time period of a simple pendulum does not depend on the mass of the bob at all. It only depends on the length of the pendulum and the acceleration due to gravity.
- Therefore, **Statement 2 is false**.

4. **Conclusion**:
- Since Statement 1 is true and Statement 2 is false, the correct answer is that Statement 1 is true and Statement 2 is false.

### Final Answer:
The correct option is **Option 3: Statement 1 is true, Statement 2 is false**.