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Q. 27

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 416

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Short Answer

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 .

See the step by step solution

Step by Step Solution

Step 1  Principles. 

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.

Step 2 Given data.

The length of the pendulum on earth is: .

Step 3  Required Data.

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

Step 4 Solutions

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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