Question

Time periodof a simple pendulum is measured at Karachi . What change will occur in the time period . If it'smeasured on mount Everest .Explain?

Answer 1

The period of the same pendulum will be longer on Mt. Everest than somewhere closer to the ground.

Explanation

Let

• $T$ be the period of this simple pendulum,
• $L$ the length of the rod holding the pendulum, and
• $g$ the gravitational field strength at the point of the pendulum.

$T \approx 2\; \pi \sqrt{\dfrac{L}{g}}$ if the pendulum swings at small angles. In other words, reducing the value of $g$ increases the length of the period.

How does the value of $g$ compare on Mt. Everest and at sea level?

$g = \dfrac{G \cdot M}{r^{2}}$,

where

• $g$ is the gravitational field strength,
• $M$ the mass of the planet earth,
• $r$ the distance away from the center of the earth, and
• $G$ is a constant.

$r$ is at the denominator. A large value of $r$ will lead to a small value of $g$. Mt. Everest is further away from the center of the earth than a spot at sea level. As a result, $g$ will be larger at the sea level and smaller on top of Mt. Everest.

Now, back to the approximation

$T \approx 2\; \pi \sqrt{\dfrac{L}{g}}$.

The value of $g$ is smaller on Mt. Everest than at sea level. As a result, the time period of the pendulum $T$ will be larger on Mt. Everest than at sea level.