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

Question 1.3:

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

Answer:

Method -1 

The given ratio is	.
Where,
G = Gravitational constant
Its unit is N m2 kg−2.
me and mp = Masses of electron and proton.
Their unit is kg.
e = Electric charge.

∈₀ = Permittivity of free space Its unit is N m² C⁻².

hence, the given ratio is dimensionless. e = 1.6 × 10⁻¹⁹ C

G = 6.67 × 10⁻¹¹ N m² kg^-2 m_e= 9.1 × 10⁻³¹ kg

m_p = 1.66 × 10⁻²⁷ kg

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.

 Method -2