• # question_answer 46) The mass of the earth is 6.00 x 1024 kg and that of the moon is $7.40\times {{10}^{22}}kg.$ The constant of gravitation $G=6.67\times {{10}^{-11}}\,N-{{m}^{2}}/k{{g}^{2}}.$The potential   energy  of  the   system  is $-7.79\times {{10}^{23}}\,J.$ The mean distance between the earth and moon is A) $~3.80\times {{10}^{8}}m$     B) $~3.37\times {{10}^{6}}m$ C) $~7.60\times {{10}^{4}}\text{ }m$      D) $~1.90\times {{10}^{2}}\text{ }m$

$U=\frac{GMm}{r}$ $\Rightarrow$ $7.79\times {{10}^{28}}$ $=\frac{6.67\times {{10}^{-11}}\times 7.4\times {{10}^{22}}\times 6\times {{10}^{24}}}{r}$ $\Rightarrow$ $r=3.8\times {{10}^{8}}\,m$