Question

If the distance between centres of the earth and the moon is $d$ and the mass of the earth is $81$ times the mass of the moon, then at what distance from centre of the earth, the gravitational field will be zero?

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

Answer 1

The correct option is C $\frac{9d}{10}$

Lets assume there is a particle of mass $m$ from $x$ distance away from earth. assuming gravitational force on $m$ is zero so :-.
Force balance
$\frac{\left(Gm81M\right)}{x^2}$ = $\frac{\left(GmM\right)}{(d-x{)}^2}$
$\frac{81}{x^2}$ = $\frac{1}{(d-x{)}^2}$
$\frac{x}{9}$ = $\frac{d-x}{1}$
solving above wquation we will get
$x=\frac{9d}{10}$