As the acceleration due to gravity increases, the time period of the simple pendulum_______

Options

A. increases
B. decreases
C. remains same
D. first increases and then decreases.

Explanation

To solve the question "As the acceleration due to gravity increases, the time period of the simple pendulum _______", we can follow these steps:

### Step 1: Understand the Time Period of a Simple Pendulum
The time period (T) of a simple pendulum is the time it takes for the pendulum to complete one full oscillation (one complete back-and-forth motion).

### Step 2: Recall the Formula for the Time Period
The formula for the time period of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where:
- \( T \) = time period
- \( L \) = length of the pendulum
- \( g \) = acceleration due to gravity

### Step 3: Analyze the Relationship Between Time Period and Gravity
From the formula, we can see that:
- The time period \( T \) is proportional to the square root of the length \( L \) and inversely proportional to the square root of the acceleration due to gravity \( g \).

This means:
\[ T \propto \frac{1}{\sqrt{g}} \]

### Step 4: Determine the Effect of Increasing Gravity
If the acceleration due to gravity \( g \) increases, the term \( \sqrt{g} \) also increases. Since \( T \) is inversely proportional to \( \sqrt{g} \), this implies that:
- As \( g \) increases, \( T \) decreases.

### Step 5: Conclusion
Thus, as the acceleration due to gravity increases, the time period of the simple pendulum decreases.

### Final Answer
The time period of the simple pendulum decreases.

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