How are proportionality constants in physical relations determined?

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SUMMARY

The values of proportionality constants in physical relations, such as the universal gravitational constant (G) and Coulomb's constant (k), are determined through meticulous experimental methods. G is noted for being the least precisely known physical constant, with varying levels of precision depending on the experimental approach. In contrast, Coulomb's constant has evolved from an empirically derived value to a precisely calculated one based on other constants. Understanding these constants requires a grasp of the experimental techniques used to measure them and their associated uncertainties.

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  • Understanding of fundamental physical constants
  • Familiarity with experimental physics methods
  • Knowledge of Coulomb's law and gravitational interactions
  • Basic grasp of precision and accuracy in measurements
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  • Research the experimental methods used to measure the universal gravitational constant (G)
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Syed Ammar
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I wanted to ask how are the values of proportionality constants in physical relations determined. How do we come to know their exact values ? An explanation with an example please...
 
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Syed Ammar said:
I wanted to ask how are the values of proportionality constants in physical relations determined. How do we come to know their exact values ? An explanation with an example please...
Which proportionality constants do you have in mind?

If you are talking about something like G (the universal gravitational constant), its value is determined through careful experiments. The value obtained is not exact (how could it be?), and there is usually a precision associated with each constant, since different experimental methods have different levels of precision associated with them. For instance, G is the one physical constant which is least precisely known.

http://en.wikipedia.org/wiki/Gravitational_constant
 
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Can you elaborate on constants of other fundamental forces like k in Coulomb's law?
 
While in the beginning, when Charles-Augustin de Coulomb postulated the law named after him, "k" had an empirically derived value, it now has a precise value, because you can calculate it from other constants. The Wikipedia article on the constant lays out the derivation quite nicely.
 

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