The mass of earth is 81 times the mass of the moon and the distance between their centres is $\mathrm{R}$.…
The mass of earth is 81 times the mass of the moon and the distance between their centres is $\mathrm{R}$. The distance from the centre of the earth where gravitational force will be zero is
$\frac{9 \mathrm{R}}{10}$
$\frac{\mathrm{R}}{2}$
$\frac{\mathrm{R}}{81}$
$\frac{\mathrm{R}}{4}$
Solution
$\mathrm{M}_{\mathrm{E}}=81 \mathrm{M}_{\mathrm{M}}$
Let at a distance $x$ from the earth, the gravitational force is zero.
$\begin{array}{c}
\therefore \frac{G M_{E}}{x^{2}}=\frac{G M_{m}}{(R-x)^{2}} \\
\frac{G 81 M_{m}}{x^{2}}=\frac{G M_{m}}{(R-x)^{2}} \\
\frac{81}{x^{2}}=\frac{1}{(R-x)^{2}} \\
\frac{9}{x}=\frac{1}{R-x} \\
9(R-x)=x \\
9 R=10 x \\
x=\frac{9}{10} R
\end{array}$
