Q. 27

Expert-verifiedFound in: Page 416

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

What is the length of a pendulum whose period on the moon matches the period of a -long pendulum on the earth?

The length of a pendulum is .

The period of an easy pendulum of length is given by,

where is that the acceleration of gravity.

Note that **the amount** of **a straightforward** pendulum depends only on its length and the magnitude of its **constant of gravitation**.

It **doesn't** **rely upon** the mass of **the item** hanging from **the sting** or the amplitude of vibration.

The length of the pendulum on earth is: .

We are asked to determine the length of a pendulum whose period on the moon equals the period of a -long pendulum on earth.

The period of the pendulum on **the planet** is found from Equation(*) :

where is the length of the earth pendulum and is the acceleration due to gravity on Earth.

**Similarly, the amount** of the pendulum on the moon is:

We know that the acceleration due to gravity on the moon is times the acceleration due to gravity on **the world**. So,

Setting Equations (1) and (2) equal, we obtain:

Square both sides:

Solve for :

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