A child is swinging on a swing in sitting position. If he stands up, then the time period of the swing will

Options

A. Increase
B. Decrease
C. Remain same
D. Increase if the child is tall and decrease if the child is short.

Answer

To solve the question about the effect of a child standing up on the swing on the time period of the swing, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Time Period**:
The time period (T) of a pendulum-like motion (which is similar to a swing) is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \(L\) is the length of the pendulum (or swing) and \(g\) is the acceleration due to gravity.

2. **Identify the Initial Condition**:
When the child is sitting on the swing, the effective length \(L\) of the swing is at a certain value, which we can denote as \(L_1\).

3. **Analyze the Change When the Child Stands Up**:
When the child stands up, the center of mass of the system changes, effectively reducing the length of the swing. We can denote this new length as \(L_2\), where \(L_2 < L_1\).

4. **Relate Length Change to Time Period**:
Since the time period is directly proportional to the square root of the length, we can express this relationship:
\[ T_1 = 2\pi \sqrt{\frac{L_1}{g}} \quad \text{(when sitting)} \]
\[ T_2 = 2\pi \sqrt{\frac{L_2}{g}} \quad \text{(when standing)} \]

5. **Compare the Time Periods**:
Since \(L_2 < L_1\), it follows that:
\[ T_2 < T_1 \]
This means that the time period decreases when the child stands up.

6. **Conclusion**:
Therefore, the correct answer is that the time period of the swing will decrease when the child stands up.

### Final Answer:
The time period of the swing will decrease.