Question

If the distance between centers of earth and moon is D and the mass of earth is 81 times the mass of moon, then at what distance from centre of earth, the gravitational force will be zero

• A. $\frac{D}{2}$
• B. $\frac{D}{3}$
• C. $\frac{9D}{10}$
• D. $\frac{9D}{8}$

Answer 1

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


If P is the point where net gravitational force is zero then $F_{PA}=F_{PB}$
$\frac{G{m}_{1}m}{x^2}=\frac{G{m}_{2}m}{(d-x{)}^2}$
By solving \(x=\frac{\sqrt{m_1}d}{\sqrt{m_1}+\sqrt{m_2}}\)
For the given problem $d=D,m_1=earth,m_2=moon$ and $m_1=81m_2\therefore m_2=\frac{m_1}{81}$
So $x=x=\frac{\sqrt{m_1}D}{\sqrt{m_1}+\sqrt{m_2}}=\frac{\sqrt{m_1}D}{\sqrt{m_1}+\sqrt{\frac{m_1}{81}}}=\frac{D}{1+\frac{1}{9}}=\frac{9D}{10}$