A pendulum clock, which keeps correct time at sea level, loses `15s` per day when taken to the top of a mountain. If the radius of the earth is `6400km`, the height of the mountain is

Explanation

To find the height of the mountain where a pendulum clock loses 15 seconds per day, we can follow these steps:

### Step 1: Understand the relationship between the time period of a pendulum and acceleration due to gravity.
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.
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