Check that the ratio ke2 / G me mp is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify? | question and answer !

Question :-

Check that the ratio ke2 / G me mp is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

Answer:-

The given ration is



Where,

G = Gravitational constant
Its unit is Nm power 2 kg power -2
me and mp = Masses of electron and proton.
Their unit is kg.
e = Electric charge
Its unit is C.
k = A constant



E0 = Permittivity of free space

Its unit is Nm power 2 C power -2.


Therefore,

 unit of the given ratio



Hence, the given ratio is dimensionless.





Hence, the numerical value of the given ratio is



This is the ratio of electric force to the gravitational force between a proton and an electron, keeping distance between them constant.