Question

The distance between the centres of the 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 $\frac{9D}{10}$

Let the net field at any point P from the earth is zero which is at distance x from the centre of the earth.
Then,the intensity of field at P due to earth $=\frac{G{M}_e}{x^2}$
the intensity of field at P due to moon $=\frac{G{M}_m}{(D-x{)}^2}$
For no intensity at P.
$\frac{G{M}_e}{x^2}=\frac{G{M}_e}{81(D-x{)}^2}$
taking root we get, $x=9(D-x)$
or $x=\frac{9D}{10}$