A simple pendulum is made of a hollow sphere having a small hole in the bottom. The pendulum is made to vibrate after filling it with water.
STATEMENT -1 `:` Time period of pendulum will first increase upto certain maximum value and then decrease are return to its initial minimum value.
and
STATEMENT-2 `:` The effective length of osciallation of a simple pendulum first increases andthen decreases toreturn to its initial minimum value

Answer

To solve the problem, we need to analyze the behavior of a simple pendulum made of a hollow sphere filled with water, focusing on the two statements provided.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a hollow sphere acting as a pendulum, which has a small hole at the bottom.
- When the pendulum is filled with water, the water can escape through the hole, affecting the pendulum's motion.

2. **Identifying the Effective Length**:
- The effective length \( L \) of the pendulum is defined as the distance from the pivot point to the center of mass (COM) of the system.
- Initially, when the sphere is full of water, the center of mass will be at a certain height.

3. **Effect of Water Level on Length**:
- As the water drains out, the center of mass of the pendulum will shift downward.
- Initially, as the water level decreases, the effective length \( L \) increases because the center of mass moves downwards, which increases the distance from the pivot to the COM.

4. **Time Period Relation**:
- The time period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
- Since \( T \) is directly proportional to the square root of the effective length \( L \), if \( L \) increases, \( T \) will also increase.

5. **Behavior of the Time Period**:
- As water continues to drain, there will be a point where the water level is half full. Beyond this point, as more water drains, the effective length \( L \) will start to decrease because the center of mass will rise.
- Consequently, the time period \( T \) will first increase (as \( L \) increases) and then decrease (as \( L \) decreases).

6. **Conclusion on Statements**:
- **Statement 1**: The time period of the pendulum will first increase up to a certain maximum value and then decrease to return to its initial minimum value. This statement is true.
- **Statement 2**: The effective length of oscillation of a simple pendulum first increases and then decreases to return to its initial minimum value. This statement is also true.

### Final Answer:
Both statements are true.