   Chapter 13, Problem 36P

Chapter
Section
Textbook Problem

A “seconds” pendulum is one that moves through its equilibrium position once each second. (The period of the pendulum is 2.000 s.) The length of a seconds pendulum is 0.992 7 m at Tokyo and 0.994 2 m at Cambridge, England. What is the ratio of the free-fall accelerations at these two locations?

To determine
The ratio of free fall accelerations at Tokyo and at Cambridge.

Explanation

Given info: The period of oscillation of both the pendulum is 2.000s . Length of the pendulum at Tokyo is 0.9927m . The length of the pendulum at Cambridge is 0.9942m .

The period of a pendulum is defined by,

T=2πLg

• T is the period
• L is the length of the string
• g is the free fall acceleration

The period of a pendulum at Tokyo is,

TT=2πLTgT

• TT is the period at Tokyo
• LT is the length of the string at Tokyo
• gT is the free fall acceleration at Tokyo

The period of a pendulum at Cambridge is,

TC=2πLCgC

• TC is the period at Cambridge
• LC is the length of the string at Cambridge

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