High School

We appreciate your visit to The period tex T tex in seconds of a pendulum is given by tex T 2 pi sqrt frac L 32 tex where tex L. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

The period [tex] T [/tex] (in seconds) of a pendulum is given by [tex] T = 2 \pi \sqrt{\frac{L}{32}} [/tex], where [tex] L [/tex] is the length of the pendulum.

Given that [tex] \pi = 3.14 [/tex] and the period is 1.57 seconds, what is the length [tex] L [/tex]?

A. 8 feet
B. 16 feet
C. 2 feet
D. 20 feet

Answer :

To find the length [tex]\( L \)[/tex] of the pendulum, we start with the formula for the period of a pendulum:

[tex]\[ T = 2\pi \sqrt{\frac{L}{32}} \][/tex]

We're given that the period [tex]\( T \)[/tex] is 1.57 seconds, and we can use [tex]\( \pi \approx 3.14 \)[/tex]. Now, let's solve for [tex]\( L \)[/tex]:

1. Substitute the given values into the formula:

[tex]\[ 1.57 = 2 \times 3.14 \times \sqrt{\frac{L}{32}} \][/tex]

2. Simplify the right side:

[tex]\[ 1.57 = 6.28 \sqrt{\frac{L}{32}} \][/tex]

3. To isolate the square root, divide both sides by 6.28:

[tex]\[ \frac{1.57}{6.28} = \sqrt{\frac{L}{32}} \][/tex]

4. Simplify the left side:

[tex]\[ 0.25 = \sqrt{\frac{L}{32}} \][/tex]

5. Remove the square root by squaring both sides:

[tex]\[ (0.25)^2 = \frac{L}{32} \][/tex]

[tex]\[ 0.0625 = \frac{L}{32} \][/tex]

6. Solve for [tex]\( L \)[/tex] by multiplying both sides by 32:

[tex]\[ L = 32 \times 0.0625 \][/tex]

[tex]\[ L = 2 \][/tex]

So, the length of the pendulum is 2 feet.

Thanks for taking the time to read The period tex T tex in seconds of a pendulum is given by tex T 2 pi sqrt frac L 32 tex where tex L. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada