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
$\frac{1}{4\,\pi \,\varepsilon_0} \cdot \frac{q \times q}{r^2} = G \frac{M_{\text{earth}} \times M_{\text{moom}}}{r^2}$
or $q=\sqrt{4 \pi \varepsilon_{0} G M_{\text {earth }} M_{\text {moon }}}$
Setting $G=6.6 \times 10^{-11} Nm ^{2} kg ^{-2}$ ;
$ M _{\text {earth }}=10^{25} kg$
and $M_{\text {moon }}=10^{23} kg$, we get
$q=8.57 \times 10^{13} C$