Question

Equal and similar charges are placed on the earth and the moon. The numerical value of charge required to neutralise their gravitational attraction is (Given: mass of earth$=6\times {10}^{24}kg$, Mass of moon$=7\times {10}^{22}kg$) :

• A. $\frac{1}{5.3}\times {10}^{-13}C$
• B. $9.3\times {10}^{13}C$
• C. $5.5\times {10}^{13}C$
• D. $3.6\times {10}^{13}C$

Answer 1

The correct option is C $5.5\times {10}^{13}C$

$\Rightarrow \frac{G{m}_e{m}_m}{r^2}=\frac{k(q{)}^2}{r^2}$

$\Rightarrow q^2=\frac{G{m}_e{m}_m}{k}$

$\Rightarrow q^2=\frac{6.67\times {10}^{-11}\times 6\times {10}^{24}\times 7\times {10}^{22}}{9\times {10}^9}$

$\Rightarrow q^2=31.1\times {10}^{26}$
$\Rightarrow q=5.5\times {10}^{13}C$