Question

If $M_e$ is the mass of earth and $M_m$ is the mass of moon $(M_e=81M_m)$. The potential energy associated with object of mass $m$ situated at a distance $R$ from the centre of earth and $r$ from the centre of moon, will be :

• A. $-Gm{M}_m[\frac{R}{81}+r]\frac{1}{R^2}$
• B. $-Gm{M}_m[\frac{81}{r}+\frac{1}{R}]$
• C. $-Gm{M}_m[\frac{81}{R}+\frac{1}{r}]$
• D. $-Gm{M}_m[\frac{81}{R}-\frac{1}{r}]$

Answer 1

The correct option is C $-Gm{M}_m[\frac{81}{R}+\frac{1}{r}]$

Gravitational $P.E=-\frac{GMm}{r}$

Gravitational $P.E$ at O= $P.E_E+P.E_m$

$P.E_o=(-\frac{G{M}_{E}m}{R})+(-\frac{G{M}_{m}m}{r})$

Given: $M_E=81M_m$

$P.E_o=-\frac{G\left(81M_m\right)m}{R}-\frac{G{M}_{m}m}{r}$

$P.E_o=-Gm{M}_m[\frac{81}{R}+\frac{1}{r}]$