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

- 1.1 km
- 2.2 km
- 3.3 km
- 4.4 km

**Solution:**

We know, the time period of a simple pendulum can be calculated by a formula:

considering length doesn’t change when taken to the top of a mountain. We can write,

(1)

Where, a) = time period on surface

b) = time period on mountain

c) = acceleration due to gravity on surface

d) = acceleration due to gravity on mountain

As acceleration due to gravity is inversely proportional to the square of the distance i.e

we can write:

(2)

From equation 1 and 2, we can write:

Finally,

According to question, pendulum loses 15 s per day: