# Q 1.3: Check that the ratio  is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

Electrostatic force

So the dimension of

..................(1)

The gravitational force between two bodies of mass M and m is

so dimension of

.............(2)

Therefor from (1) and (2)

is dimensionless

or

Here,

K = , where  is the permittivity of space.

e = Electric charge ([e] = [C])

G = Gravitational constant. ([G]=  )

and  are mass of electron and proton ([] = []  = [Kg])

Substituting these units, we get

Hence, this ratio is Dimensionless.

Putting the value of the constants

The given ratio is the ratio of electric force to the gravitational force between an electron and a proton  considering the distance between them is constant!

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