Calculate the ratio of time periods of pendulam A of length 50 cm and pendulam  B of length 2 m

The time period \( T \) of a simple pendulum is given by the formula:

\[
T = 2\pi \sqrt{\frac{L}{g}}
\]

where:
- \( T \) is the time period,
- \( L \) is the length of the pendulum,
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).

We are asked to find the ratio of the time periods of pendulum A and pendulum B.

Let:
- \( L_A = 50 \, \text{cm} = 0.5 \, \text{m} \) (for pendulum A),
- \( L_B = 2 \, \text{m} \) (for pendulum B).

The ratio of the time periods \( \frac{T_A}{T_B} \) is given by:

\[
\frac{T_A}{T_B} = \frac{2\pi \sqrt{\frac{L_A}{g}}}{2\pi \sqrt{\frac{L_B}{g}}} = \sqrt{\frac{L_A}{L_B}}
\]

Substituting the values:

\[
\frac{T_A}{T_B} = \sqrt{\frac{0.5}{2}} = \sqrt{0.25} = 0.5
\]

Thus, the ratio of the time periods is:

\[
\frac{T_A}{T_B} = 0.5
\]

So, the time period of pendulum A is half that of pendulum B.

Would you like more details or have any questions?

Here are 5 related questions to further your understanding:
1. How does the length of a pendulum affect its time period?
2. What happens to the time period of a pendulum if you double its length?
3. How does the time period of a pendulum change in different gravitational fields?
4. What is the relationship between frequency and time period of a pendulum?
5. Can the mass of the bob affect the time period of a pendulum?

**Tip:** The time period of a pendulum is independent of the mass and only depends on the length and gravity.

Calculate the ratio of time periods of pendulum A of length 50 cm and pendulum B of length 2 m

Find out how to calculate the time period ratio of pendulums A (50 cm) and B (2 m) using the formula T = 2π√(L/g). This problem explains the relationship between the length of a pendulum and its time period. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation