Newton’s law of universal gravitation is represented by F=(G M m)/(r^2) Here F is the magnitude

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Newton’s law of universal gravitation is represented by F=(G...

Newton’s law of universal gravitation is represented by $$F=\frac{G M m}{r^{2}}$$ Here $F$ is the magnitude of the gravitational force exerted by one small object on another, $M$ and $m$ are the masses of the objects, and $r$ is a distance. Force has the SI units $\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}^{2}$. What are the SI units of the proportionality constant $G ?$

Newton’s law of universal gravitation is represented by
$$F=\frac{G M m}{r^{2}}$$
Here $F$ is the magnitude of the gravitational force exerted by one small object on another, $M$ and $m$ are the masses of the objects, and $r$ is a distance. Force has the SI units $\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}^{2}$. What are the SI units of the proportionality constant $G ?$

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Key Concepts

Proportionality Constant

A proportionality constant is a factor in physical equations that ensures the relationship between variables is dimensionally consistent. In equations like Newton's law of universal gravitation, this constant adjusts the relationship by providing the necessary scaling factor so that the units on both sides of the equation match, thereby defining its own unit in terms of the basic SI units.

Dimensional Analysis

Dimensional analysis is a technique used to ensure that equations describing physical phenomena are consistent by matching the dimensions on both sides of the equation. It allows us to determine the appropriate units of any constant in an equation by requiring that the overall units balance, which is crucial for the integrity of physical laws.

SI Units

The International System of Units (SI) is the standard set of units for measuring physical quantities. It defines base units such as the kilogram for mass, meter for length, and second for time. By expressing all terms in their base SI units, one can systematically determine the correct units for derived quantities and constants.

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