 # The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is given by T = 2π l g where ℓ is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent. (You might want to check the formula using your keys at the end of a string and a stopwatch.) ### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300 ### College Physics

11th Edition
Raymond A. Serway + 1 other
Publisher: Cengage Learning
ISBN: 9781305952300

#### Solutions

Chapter
Section
Chapter 1, Problem 1P
Textbook Problem
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## The period of a simple pendulum, defined as the time necessary for one complete oscillation, is measured in time units and is given by T =  2π l g where ℓ is the length of the pendulum and g is the acceleration due to gravity, in units of length divided by time squared. Show that this equation is dimensionally consistent. (You might want to check the formula using your keys at the end of a string and a stopwatch.)

Expert Solution
To determine

The dimensional consistency of the time period equation

### Explanation of Solution

The formula to calculate the consistency of a dimension is,

T=2πl/g

Here,

T is the time period,

l is the length

g is the gravitational acceleration

Substitute T for T, L for l,  (L/T2) for g to check the dimensional consistency.

[T]=[l][g

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