A simple pendulum has a hollow sphere containing mercury suspended by means of a wire. If a little mercury is drained off, the period of the pendulum will

Options

A. remains unchanged
B. increase
C. decrease
D. becomes zero

Explanation

To solve the problem regarding the effect of draining mercury from a hollow sphere pendulum on its period, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Pendulum**:
A simple pendulum consists of a mass (the bob) suspended from a fixed point by a wire. The period of a pendulum is influenced by the length of the pendulum and the acceleration due to gravity.

2. **Formula for the Period**:
The formula for the period \( T \) of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \( L \) is the length from the pivot to the center of mass of the bob, and \( g \) is the acceleration due to gravity.

3. **Effect of Draining Mercury**:
Initially, the hollow sphere is filled with mercury, and the center of mass is at a certain position. When some mercury is drained, the mass of the bob decreases, and the center of mass of the bob shifts downward.

4. **Change in Length**:
As mercury is drained, the effective length \( L \) (the distance from the pivot to the center of mass) increases. This is because the center of mass of the hollow sphere will now be lower than it was when it was full of mercury.

5. **Analyzing the Period Change**:
Since the period \( T \) is directly proportional to the square root of the length \( L \), if \( L \) increases, the period \( T \) will also increase. Therefore, we can conclude that:
\[ \text{If } L \text{ increases, then } T \text{ increases.} \]

6. **Conclusion**:
After draining some mercury, the period of the pendulum will increase. Thus, the correct answer is that the period of the pendulum will increase.

### Final Answer:
The period of the pendulum will **increase**.

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