Question

If $M _{e}$ is the mass of earth and $M _{ m }$ is the mass of moon $\left( M _{e}=81\, M _{ m }\right)$. The potential energy of an object of mass $m$ situated at a distance $R$ from the centre of earth and $r$ from the centre of moon, will be :-

• A. $- GmM _{ m }\left(\frac{ R }{81}+ r \right) \frac{1}{ R ^{2}}$
• B. $- GmM _{e}\left(\frac{81}{ r }+\frac{1}{ R }\right)$
• C. $-GmM_{ m }\left(\frac{81}{ R }+\frac{1}{ r }\right)$
• D. $GmM _{ m }\left(\frac{81}{ R }-\frac{1}{ r }\right)$

Answer 1

Answer: (C)

$=-\frac{G M_{e} m}{R}-\frac{G M_{m} m}{r}$
$=-\frac{G\left(81 M_{m}\right) m}{R}-\frac{G M_{m} m}{r}$
$=-G m M_{m}\left(\frac{81}{R}+\frac{1}{r}\right)$