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

Options

A. (a)increase
B. (b)decrease
C. (c)remain the same
D. (d)increase if the child is long and decrease 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 of a pendulum
The time period \( T \) of a simple pendulum 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,
- \( g \) is the acceleration due to gravity.

### Step 2: Analyze the situation when the child is sitting
When the child is sitting on the swing, the effective length \( L \) is the distance from the pivot point (the top of the swing) to the center of mass of the child.

### Step 3: Consider the change when the child stands up
When the child stands up, the center of mass of the child rises. This means that the effective length \( L \) of the pendulum decreases.

### Step 4: Relate the change in length to the time period
Since \( T \) is proportional to the square root of \( L \), if \( L \) decreases, \( T \) will also decrease. This can be expressed as:
- If \( L \) decreases, then \( T \) decreases.

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

### Final Answer
The time period of the swing will **decrease** when the child stands up.