Chapter 25, Problem 56A

The period of a simple pendulum is given by $T=2\pi \sqrt{\frac{L}{g}}$, where g is the acceleration of gravity and L is the length of the pendulum. In a lab, you want to double the period of a certain pendulum. Your friend says you'll have to make the pendulum twice as long. Do you agree with your friend?

To determine

To explain: Whether a person agrees with his friend or not.

Answer to Problem 56A

No, a person will not agree with his friend.

Explanation of Solution

Given:

It is required to double the time period.

Formula used:

For a simple pendulum, time period is,

  $T=2\pi \sqrt{\frac{L}{g}}$ .

Where, L is length, and g is acceleration due to gravity.

Calculation:

From the formula, it is observed that time period is proportional to the square root of the length of the pendulum.

So if someone wants to double the time period, the length must be 4 times as before.

As the square root of 4 is 2. Only then the time period can be double .

Conclusion:

Therefore, a person will not agree with his friend.