A boy is swinging in a swing. If he stands , the time period will

Options

A. First decreases,then increases
B. Decreases
C. Increases
D. Remains same

Answer

To solve the question about how the time period of a swing changes when a boy stands up, we can follow these steps:

### Step 1: Understand the Concept of Time Period
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 (the distance from the pivot to the center of mass),
- \( g \) is the acceleration due to gravity.

### Step 2: Analyze the Situation
When the boy is sitting on the swing, the effective length \( l \) is the distance from the pivot point of the swing to the center of mass of the boy. When he stands up, his center of mass rises, effectively reducing the length \( l \).

### Step 3: Determine the Effect on Length
Since the boy's center of mass moves up when he stands, the effective length \( l \) of the swing decreases.

### Step 4: Relate Length to Time Period
From the time period formula, we can see that if \( l \) decreases, then \( T \) must also decrease because \( T \) is directly proportional to the square root of \( l \).

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

The correct answer is: **decrease**.

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