The period of a pendulum, T, is assumed (correctly or incorrectly) to depend on the mass, M, the...

Question:

The period of a pendulum, T, is assumed (correctly or incorrectly) to depend on the mass, M, the length of the pendulum, L, the acceleration due to gravity, G, and the angle of swing, θ.

Using dimensional analysis, nondimensionalize the period, T, and express its dependence on the other non-dimensional terms.

Dimensional analysis

According to dimensional analysis, the dimensions of a physical quantity must be equal to the dimensions of the physical quantities upon which it has a direct relationship.

Answer and Explanation:

The dependency of the time period is given as,

{eq}\begin{align*} {\rm{T}} &\propto {{\rm{M}}^x}{{\rm{L}}^y}{{\rm{G}}^z}{{\rm{\theta...

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Unit Conversion and Dimensional Analysis

from Chemistry 101: General Chemistry

Chapter 1 / Lesson 2
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