Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Problem 45

Find the relationship between the time period of the pendulum and the length of the pendulum.

Short Answer

Expert verified
Answer: The time period of a pendulum (T) is directly proportional to the square root of its length (L). The relationship between T and L can be expressed as T ∝ √(L), or using the formula T = 2π√(L/g), where g is the acceleration due to gravity.

Step by step solution

01

Recall the formula for the time period of a simple pendulum

The formula for the time period (T) of a simple pendulum is: T = 2π√(L/g)
02

Express the relationship between the time period and the length using the formula

To find the relationship between T and L, we simply need to observe the formula: T = 2π√(L/g) Here, we can see that the time period (T) is proportional to the square root of the length of the pendulum (L). The constant of proportionality is given by 2π√(1/g).
03

Write the final relationship between the time period and the length

The relationship between the time period (T) of a pendulum and its length (L) can be expressed as: T ∝ √(L) Or in terms of the formula: T = 2π√(L/g) This shows that the time period of a pendulum is directly proportional to the square root of its length, with the constant of proportionality being 2π√(1/g).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Match the entries given in column \(A\) with the appropriate ones in column \(\mathrm{B}\).

The ratio of unit of acceleration and velocity gives unit of the physical quantity _ (1) time (2) frequency (3) amplitude (4) speed

Two hour is equal to __ seconds.

Mention the different units of time and speed.

In a race, two athletes 'A' and 'B' reach the finishing point in 20 second and 22 second respectively. (a) What is the ratio of their speeds? (b) If both are allowed to run with their respective speeds for a given time, what is the ratio of the distance covered by them?
See all solutions

Recommended explanations on Physics Textbooks

Classical Mechanics

Read Explanation

Electricity

Read Explanation

Particle Model of Matter

Read Explanation

Turning Points in Physics

Read Explanation

Measurements

Read Explanation

Space Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free