Problem 5: How many electrons should be removed from each of the two similar spheres each of 10g so that electrostatic repulsion be balanced by gravitational force?

Solution:

Step: 1 Overview

See the overviews of Problem-1 and Problem-2.

Step: 2 Calculation

We know that gravitational force is equal to Gm₁m₂/r² and also electrostatic force is equal to Kq₁q₂/r².
Since both are equal so,

Gm₁m₂/r² = Kq₁q₂/r²
Multiplying r² both sides,
Gm₁m₂ = Kq₁q₂

since m1=m2=0.01Kg, G=6.67x10^-11, K=9x10⁹ and q1=q2 so,

(6.67x10^-11)(0.01)² = (9x10⁹)q²
6.67x10^-15 = (9x10⁹)q²
q² = (6.67x10^-15)/(9x10⁹)
q² = 0.741x10^-24
q = 0.86x10^-12

q is charge and we have to find number of electrons (n), this can be done by the formula:

q = ne, where n is a number of electrons and e is charge of electron.
n = q/e
n = (0.86x10^-12)/(1.6x10^-19)
n = 0.537x10⁷
n = 5.37x10⁶ (Ans)