A simple pendulum is taken from the equator to the pole. Its period

Options

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

Answer

To solve the problem of how the period of a simple pendulum changes when it is taken from the equator to the pole, we can follow these steps:

### Step 1: Understand the formula for the period of a simple pendulum
The period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g_{\text{effective}}}} \]
where:
- \( L \) is the length of the pendulum,
- \( g_{\text{effective}} \) is the effective acceleration due to gravity.

### Step 2: Determine the effective gravity at the equator and the pole
At the equator, the effective gravity \( g_{\text{effective}} \) is affected by the centrifugal force due to the Earth's rotation. The formula for effective gravity at the equator is:
\[ g_{\text{effective, equator}} = g - \omega^2 R \]
where:
- \( g \) is the standard acceleration due to gravity,
- \( \omega \) is the angular velocity of the Earth,
- \( R \) is the radius of the Earth.

At the poles, there is no centrifugal force acting on the pendulum, so:
\[ g_{\text{effective, pole}} = g \]

### Step 3: Compare the effective gravity at the equator and the pole
Since \( \omega^2 R \) is a positive value, we have:
\[ g_{\text{effective, equator}} < g_{\text{effective, pole}} \]
This means that the effective gravity at the equator is less than that at the pole.

### Step 4: Analyze the effect on the period of the pendulum
Since the period \( T \) is inversely proportional to the square root of \( g_{\text{effective}} \), we can conclude:
\[ T_{\text{equator}} > T_{\text{pole}} \]
This implies that the period of the pendulum at the equator is greater than the period at the pole.

### Step 5: Conclusion
As the pendulum is taken from the equator to the pole, the period decreases. Therefore, the correct answer is that the period of the pendulum decreases when moving from the equator to the pole.

### Final Answer
The period of a simple pendulum decreases when taken from the equator to the pole.

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