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.

Step-by-step 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{(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 = (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{(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.