Question

If the distance between the centres of earth and moon is $D$ and mass of earth is $81$ times that of moon. At what distance from the centre of earth gravitational field will be zero.

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

Answer 1

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

Given:

$M_m=m{M}_e=81m$

Let the distance $x$ from earth where gravitational field is zero.

Then,

$\frac{G8m}{x^2}=\frac{Gm}{{(D-x)}^2}$

$\frac{x}{D-x}=9$

$x=\frac{9}{10}D$

Answer is $\frac{9}{10}D$