A simple pendulum is transferred from the earth to the moon. Assuming its time period is inversely proportional to the square root of acceleration due to gravity, it will

Options

A. Become faster
B. Become slower
C. Remain the same
D. Be sometimes faster, sometimes slower

Answer

To solve the problem, we need to analyze how the time period of a simple pendulum changes when it is transferred from Earth to the Moon.

### Step-by-Step Solution:

1. **Understanding 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 \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.

2. **Inversely Proportional Relation**:
According to the problem, the time period \( T \) is inversely proportional to the square root of the acceleration due to gravity \( g \). This means:
\[ T \propto \frac{1}{\sqrt{g}} \]
Therefore, we can express this relationship as:
\[ T = k \cdot \frac{1}{\sqrt{g}} \]
where \( k \) is a constant.

3. **Acceleration Due to Gravity on Earth and Moon**:
The acceleration due to gravity on Earth is approximately \( g_e \approx 9.81 \, \text{m/s}^2 \). On the Moon, the acceleration due to gravity \( g_m \) is:
\[ g_m = \frac{g_e}{6} \approx \frac{9.81}{6} \approx 1.635 \, \text{m/s}^2 \]

4. **Calculating Time Period on Earth and Moon**:
- **Time Period on Earth**:
\[ T_e = k \cdot \frac{1}{\sqrt{g_e}} \]
- **Time Period on Moon**:
\[ T_m = k \cdot \frac{1}{\sqrt{g_m}} = k \cdot \frac{1}{\sqrt{\frac{g_e}{6}}} = k \cdot \frac{\sqrt{6}}{\sqrt{g_e}} = \sqrt{6} \cdot T_e \]

5. **Comparing Time Periods**:
Since \( \sqrt{6} \) is greater than 1, we have:
\[ T_m = \sqrt{6} \cdot T_e \quad (\text{where } \sqrt{6} \approx 2.45) \]
This means that the time period on the Moon is approximately 2.45 times longer than that on Earth.

6. **Conclusion**:
Since the time period increases when moving from Earth to the Moon, the pendulum will take longer to complete one oscillation. Therefore, we conclude that the pendulum becomes slower when transferred to the Moon.

### Final Answer:
The correct option is: **becomes slower**.

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