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

Options

A. increase.
B. decrease.
C. remains same.
D. increases if the child is long and decreases if the child is short.

Explanation

To solve the problem of how the time period of a swing changes when a child standing up, we can follow these steps:

### Step 1: Understand the Time Period Formula
The time period \( T \) of a simple pendulum (which is analogous to the swing) is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where:
- \( T \) is the time period,
- \( L \) is the length of the pendulum (distance from the point of suspension to the center of mass),
- \( g \) is the acceleration due to gravity.

### Step 2: Identify Changes in Length
When the child is sitting on the swing, the length \( L \) is the distance from the point of suspension to the center of mass of the child. When the child stands up, the center of mass of the system (the child and the swing) changes. Specifically, the effective length \( L' \) from the point of suspension to the new center of mass will decrease.

### Step 3: Compare the Two Lengths
Since the child is now standing, the new length \( L' \) is less than the original length \( L \):
\[ L' < L \]

### Step 4: Analyze the Effect on Time Period
From the time period formula, if \( L' < L \), then:
\[ T' = 2\pi \sqrt{\frac{L'}{g}} < 2\pi \sqrt{\frac{L}{g}} = T \]
This means that the new time period \( T' \) when the child stands up is less than the original time period \( T \).

### Step 5: Conclusion
Thus, when the child stands up on the swing, the time period of the swing decreases.

### Summary
- The time period of a swing is dependent on the length of the pendulum.
- Standing up reduces the effective length of the swing.
- A shorter length results in a shorter time period.