Question

The mass of the earth is $6\times 10^{24}kg$ and that of the moon is $7.4\times 10^{22}kg$. The potential energy of the system is $-7.79\times 10^{28}J$. The mean distance between the earth and moon is
$(G=6.67\times 10^{-11}N{m}^{2}k{g}^{-2})$

• A. $3.8\times 10^{8}m$
• B. $3.37\times 10^{6}m$
• C. $7.60\times 10^{4}m$
• D. $1.9\times 10^{2}m$

Answer 1

Answer: (A)

Here, Potential energy of system,
$U=-7.79\times 10^{28}J$
Mass of the earth, $M_E=6\times 10^{24}kg$
Mass of the moon, $M_M=7.4\times 10^{22}kg$
The potential energy of the earth-moon system is
$U=-\frac{G{M}_E{M}_M}{r}$
where $r$ is the mean distance between earth and moon.
$\therefore r=-\frac{G{M}_E{M}_M}{U}$
$=-\frac{6.67\times 10^{-11}\times 6\times 10^{24}\times 7.4\times 10^{22}}{-7.79\times 10^{28}}$
$=3.8\times 10^{8}m$