The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

Options

A. first increase and then decrease to the original value
B. first decrease and then increase to the original value
C. remain unchanged
D. increase towards a saturation value

Explanation

To solve the problem, we need to analyze how the time period of a simple pendulum changes when the bob is a hollow ball filled with water and a hole at the bottom is unplugged.

### Step-by-Step Solution:

1. **Understand 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 (distance from the pivot to the center of mass of the bob) and \( g \) is the acceleration due to gravity.

2. **Initial Condition:**
Initially, when the bob is filled with water and the hole is plugged, the length \( l \) is at its original value.

3. **Effect of Unplugging the Hole:**
When the hole is unplugged, water starts to flow out of the bob. As the water exits, the mass of the bob decreases, and the center of mass of the bob shifts downward. This results in an effective increase in the length \( l \) of the pendulum.

4. **New Length During Water Flow:**
If we denote the change in length due to the outflow of water as \( \Delta l \), the new length of the pendulum becomes:
\[ l' = l + \Delta l \]
Consequently, the new time period \( T' \) becomes:
\[ T' = 2\pi \sqrt{\frac{l + \Delta l}{g}} \]
Since \( \Delta l > 0 \), it follows that \( T' > T \). Therefore, the time period increases while water is flowing out.

5. **Final Condition After Water is Empty:**
Once all the water has drained out, the bob returns to its original state, and the length of the pendulum returns to \( l \). Thus, the time period returns to its original value:
\[ T'' = 2\pi \sqrt{\frac{l}{g}} = T \]

6. **Conclusion:**
During the time the water is flowing out, the time period of the pendulum increases, and once the water is completely drained, it returns to its original time period.

### Final Answer:
The time period of oscillation would first increase while the water is coming out and then return to its original value once the water is completely drained.

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