## College Physics (4th Edition)

$2.7\times 10^9$ electrons must be removed from each sphere.
We can find an expression for the gravitational force: $F = \frac{G~m~m}{r^2}$ We can find an expression for the magnitude of the electric force: $F = \frac{k~q~q}{r^2}$ We can equate the two forces to find the required charge $q$ on each sphere: $\frac{k~q~q}{r^2} = \frac{G~m~m}{r^2}$ $q^2 = \frac{G~m^2}{k}$ $q = \sqrt{\frac{G~m^2}{k}}$ $q = \sqrt{\frac{(6.67\times 10^{-11}~N~m^2/kg^2)~(5.0~kg)^2}{9.0\times 10^9~N~m^2/C^2}}$ $q = 4.3\times 10^{-10}~C$ We can find the number of electrons which must be removed from each sphere: $\frac{-4.3\times 10^{-10}~C}{-1.6\times 10^{-19}~C} = 2.7\times 10^9$ $2.7\times 10^9$ electrons must be removed from each sphere.