Question

Mass of the earth is 81 times the mass of the moon and distance between the earth and moon is 60 times the radius of the earth. If R is radius of the earth, then distance between the moon and the point on the line joining the moon and earth where the gravitational force becomes zero is

• A. 30R
• B. 15R
• C. 6R
• D. 5R

Answer 1

The correct option is C 6R

Let m be the mass at a distance x from the centre of the moon where gravitation force is zero.
$\therefore \frac{G{M}_{e}m}{(60R-x{)}^2}=\frac{G{M}_{moon}m}{x^2}$
or $\frac{81}{(60R-x{)}^2}=\frac{1}{x^2}$ or $\frac{9}{60R-x}=\frac{1}{x}$
or $x=6R$