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

Respuesta :

jacob193

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

Explanation

Let

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

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

How does the value of [tex]g[/tex] compare on Mt. Everest and at sea level?

[tex]g = \dfrac{G \cdot M}{r^{2}}[/tex],

where

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

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

Now, back to the approximation

[tex]T \approx 2\; \pi \sqrt{\dfrac{L}{g}}[/tex].

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

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