A pendulum clock keeping correct time is taken to high altitudes

Options

A. it will keep correct time
B. its length should be increased to keep correct time
C. its length should be decresed to keep correct time
D. it cannot keep correct time even if the length is changed

Answer

To solve the problem of how a pendulum clock behaves when taken to high altitudes, we need to analyze the relationship between the pendulum's time period, the acceleration due to gravity (g), and the length of the pendulum (L).

### 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. **Effect of Altitude on Gravity:**
As we take the pendulum clock to higher altitudes, the value of \(g\) decreases. This is because gravity decreases with altitude, following the formula:
\[ g = \frac{GM}{(R + h)^2} \]
where \(G\) is the gravitational constant, \(M\) is the mass of the Earth, \(R\) is the radius of the Earth, and \(h\) is the height above the Earth's surface.

3. **Impact on Time Period:**
Since \(g\) decreases at higher altitudes, we can see from the formula for the time period that if \(g\) decreases, the time period \(T\) will increase (because \(T\) is inversely proportional to the square root of \(g\)).

4. **Maintaining Correct Time:**
To keep the pendulum clock keeping correct time, we need to adjust the length \(L\) of the pendulum. Since \(T\) is increasing due to the decrease in \(g\), we need to decrease \(L\) to keep \(T\) constant.

5. **Conclusion:**
Therefore, to maintain the correct time at high altitudes, the length of the pendulum should be decreased.

### Final Answer:
The length should be decreased to keep the correct time.

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