When a boy is playing on a swing in the sitting position , the time period of oscillations of the swing is T. If the boy stands up , the time period of oscillation of the spring will be

Options

A. more than T
B. less than T
C. equal to T
D. Cannot be predicted

Explanation

To solve the problem, we need to analyze how the time period of oscillation of a swing changes when the boy goes from a sitting position to a standing position.

### Step-by-Step Solution:

1. **Understanding the Time Period of a 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 from the pivot point to the center of mass of the pendulum,
- \( g \) is the acceleration due to gravity.

2. **Identifying the Initial Condition**:
When the boy is sitting on the swing, the center of mass of the system (boy + swing) is at a certain height, which we denote as \( L \). The time period of oscillation in this position is given as \( T \).

3. **Analyzing the Change in Position**:
When the boy stands up, the center of mass of the system changes. The effective length \( L' \) from the pivot to the new center of mass when the boy is standing is less than \( L \) because the boy's height is reduced relative to the swing's pivot.

4. **Comparing Lengths**:
Since the boy is now standing, the effective length \( L' < L \).

5. **Effect on Time Period**:
Since the time period \( T \) is directly proportional to the square root of the length:
\[ T' = 2\pi \sqrt{\frac{L'}{g}} \]
and since \( L' < L \), it follows that:
\[ T' < T \]
Therefore, the time period of oscillation when the boy stands up is less than \( T \).

6. **Conclusion**:
The time period of oscillation of the swing when the boy stands up is less than \( T \).

### Final Answer:
The time period of oscillation of the swing when the boy stands up will be **less than T**.