Question

The distance of the centres of moon and the earth is D. The mass of the earth is 81 times the mass of the moon. At what distance from the centre of the earth, the gravitational force will be zero:

• A. $\frac{D}{2}$
• B. $\frac{2D}{3}$
• C. $\frac{4D}{3}$
• D. $\frac{9D}{10}$

Answer 1

The correct option is D $\frac{9D}{10}$

gravitational force is given by $F=\frac{GMm}{R^2}$

so for force to be zero let distance from center of earth is $x$

then $\frac{G{M}_{e}m}{x^2}=\frac{G{M}_{m}m}{(D-x{)}^2}$

$=>\frac{81M_o}{x^2}=\frac{M_o}{(D-x{)}^2}$

after solving we get $x=\frac{9D}{10}$

so option D is best possible answer.