A simple pendulum is made of bob which is a hollow sphere full of sand suspended by means of a wire. If all the sand is drained out, the period of the pendulum will

Options

A. increase
B. decrease
C. remian same
D. become erratic

Explanation

To solve the problem, we need to analyze the situation of a simple pendulum with a bob that is initially a hollow sphere filled with sand. We will then consider the effect of draining the sand on the period of the pendulum.

### Step-by-Step Solution:

1. **Understanding the Pendulum**:
- A simple pendulum consists of a mass (the bob) attached to a string or wire of length \( L \).
- The period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \( g \) is the acceleration due to gravity.

2. **Initial Condition with Sand**:
- When the bob is filled with sand, it has a certain mass \( m \).
- The period of the pendulum in this state can be expressed as:
\[ T_1 = 2\pi \sqrt{\frac{L}{g}} \]

3. **Condition After Draining the Sand**:
- When the sand is drained out, the mass of the bob decreases to \( m' \), where \( m' < m \).
- However, the length of the pendulum \( L \) and the acceleration due to gravity \( g \) remain unchanged.

4. **Period After Draining the Sand**:
- The period of the pendulum after the sand is drained can be expressed as:
\[ T_2 = 2\pi \sqrt{\frac{L}{g}} \]
- Notice that this expression is the same as \( T_1 \).

5. **Conclusion**:
- Since the period \( T \) of a simple pendulum does not depend on the mass of the bob, the period remains the same before and after the sand is drained.
- Therefore, the period of the pendulum will remain unchanged.

### Final Answer:
The period of the pendulum will remain the same after all the sand is drained out.

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