Question

What is the unique property shown by the charge of an oil drop?

Answer 1

Charge of an oil drop shows that it was quantized, always a multiple of $-1.6\times {10}^{-19}C$ i.e. charge of single electron.
A balance of the electrostatic force and gravitational force on the oil drop helped to give us an estimate of the charge $q$ by:
$mg=qE$
$q=\frac{mg}{E}$
$E$ is the electric field and $mg$ is the weight of the drop.