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nishanth R
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Homework Statement
What is the difference between a dimensional physical constant and dimensionless physical constant?
Dimensional physical constants are physical quantities that have both a numerical value and a unit of measurement, such as speed (meters per second) or energy (joules). Dimensionless physical constants, on the other hand, are numerical values that do not have any associated units.
One example is the gravitational constant, denoted by G, which has a value of approximately 6.67 x 10^-11 m^3/(kg*s^2). It is used in the calculation of gravitational force between two objects.
One example is the fine structure constant, denoted by α (alpha), which has a value of approximately 1/137. It is a dimensionless number that relates the strength of the electromagnetic interaction between elementary particles.
It is important because dimensional physical constants are affected by the units of measurement used, while dimensionless physical constants are not. This means that different unit systems can lead to different numerical values for dimensional physical constants, but the value of dimensionless physical constants remains the same regardless of the unit system. This can have significant implications in scientific calculations and experiments.
No, there are also semi-dimensionless physical constants which have both a numerical value and a unit, but the unit cancels out when used in a specific equation. An example of this is the speed of light, denoted by c, which has a value of approximately 3 x 10^8 m/s. It is used in the equation E=mc^2, where the units of mass and energy cancel out leaving the speed of light as a pure number.