Question

What equal charges would have to be placed on earth and moon to neutralize their gravitational force of attraction? Given that mass of earth $=10^{25}kg$ and mass of moon $=10^{23}kg$

• A. $8.57\times 10^{16}C$
• B. $8.57\times 10^{13}C$
• C. $5.45\times 10^{13}C$
• D. $5.45\times 10^{16}C$

Answer 1

Answer: (B)

If $q$ is charge on the earth and the moon, then
$\frac{1}{4\pi {\epsilon }_0}\cdot \frac{q\times q}{r^2}=G\frac{M_{\text{earth}}\times M_{\text{moom}}}{r^2}$
or $q=\sqrt{4\pi {\epsilon }_{0}G{M}_{\text{earth }}{M}_{\text{moon }}}$
Setting $G=6.6\times 10^{-11}N{m}^{2}k{g}^{-2}$ ;
$M_{\text{earth }}=10^{25}kg$
and $M_{\text{moon }}=10^{23}kg$, we get
$q=8.57\times 10^{13}C$