If a pendulum clock is shifted from earth to the surface of moon. Then it

Options

A. loses time
B. gains time
C. keeps correct time
D. does not function

Answer

To solve the problem of what happens to a pendulum clock when it is shifted from Earth to the surface of the Moon, we need to analyze the time period of the pendulum clock using the formula for the time period of a simple pendulum.

### Step 1: Understand the formula for 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: Identify the change in gravitational acceleration
On Earth, the acceleration due to gravity \( g \) is approximately \( 9.81 \, \text{m/s}^2 \). On the Moon, the gravitational acceleration is about \( \frac{g}{6} \), which is approximately \( 1.62 \, \text{m/s}^2 \).

### Step 3: Analyze the time period on the Moon
Since the length of the pendulum \( L \) remains constant when moving from Earth to the Moon, we can express the new time period \( T' \) on the Moon as:
\[ T' = 2\pi \sqrt{\frac{L}{g/6}} = 2\pi \sqrt{\frac{6L}{g}} \]
This shows that the time period on the Moon \( T' \) is greater than the time period on Earth \( T \).

### Step 4: Compare the time periods
Since \( T' = 2\pi \sqrt{\frac{6L}{g}} \) is greater than \( T = 2\pi \sqrt{\frac{L}{g}} \), we conclude that:
\[ T' > T \]
This means that the pendulum will take longer to complete one oscillation on the Moon compared to on Earth.

### Step 5: Determine the effect on timekeeping
If the time period of the pendulum increases, it means that the clock will take longer to complete each second. Therefore, the pendulum clock will lose time. For example, if it should show 1 second, it may show 1.1 seconds instead.

### Conclusion
When a pendulum clock is shifted from Earth to the surface of the Moon, it will lose time because the time period of the pendulum increases due to the lower gravitational acceleration on the Moon.

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