# Question #60d4a

Jul 17, 2016

Constant of proportionality basically comes from mathematics.
In Physics and other branches of Science or Subjects it is applied and used to describe variables.

If change in one variable is always accompanied by a change in another variable, and if the changes between the two are always related by a constant multiplier, two variables are termed as proportional to each other. And the constant multiplier is called the constant of proportionality.

1. If one variable $y$ is always the product of another variable $x$ and a constant $C$, the two are said to be directly proportional. In this case $y$ and $x$ are directly proportional if the ratio $\frac{y}{x} = C$.
Symbolically, this is written as $y \propto x$.
Mathematically, we write an equation $y = C x$,
where $C$ is the constant of proportionality.
2. If the product of the two variables $x \mathmr{and} y$ is always a constant, then two are said to be inversely proportional to each other. For example $x \mathmr{and} y$ are inversely proportional if the product $x y = {C}_{1}$ is constant.
Symbolically, this is written as $y \propto \frac{1}{x}$.
Mathematically, we write an equation $y = {C}_{1} \frac{1}{x}$,
where ${C}_{1}$ is the constant of proportionality.

Example: In this particular example both direct as well inverse proportion is in one equation.

Law of Universal Gravitation states that the force of attraction $F$ between two bodies is directly proportional to the product of masses of the two bodies. It is also inversely proportional to the square of the distance between the two bodies.

Mathematically

$F \propto {M}_{1.} {M}_{2}$
Also $F \propto \frac{1}{r} ^ 2$
Combining the two we obtain the proportionality expression

$F \propto \frac{{M}_{1.} {M}_{2}}{r} ^ 2$
Follows that

$F = G \frac{{M}_{1.} {M}_{2}}{r} ^ 2$

Where $G$ is constant of proportionality.
It has the value $6.67408 \times {10}^{-} 11 {m}^{3} k {g}^{-} 1 {s}^{-} 2$ and also called Universal Gravitational Constant.

Jul 30, 2017

More generally the constant allows you to move from a proportionality (w $\propto$ m) to an equation (w = m x g) as explained above.