Check that the ratio `(ke^(2))/(Gm_(e)m_(p))` is dimensionless. Look up a table of physical constants and determine the value of this ratio. What does the ratio signify ?

Explanation

Given ratio is `(ke^(2))/(Gm_(e)m_(p))`………(1)
Now, above ratio is equivalent to,
`((ke^(2))/(r^(2)))/((Gm_(e)m_(p))/r^(2)) =- F_(e)/F_(g)`
Obviously above ratio is unitless and hence dimensionless because it is a ratio of two identical physical quantities.