The acceleration due to gravity at Moon Surface is g6 . If radius of Moon is 3R11 mass of moon is 3Mx Find ‘x’ (where g is the acceleration due to gravity on earth surface, R is radius of earth, M is the mass of earth)

g6=Gm3R112⇒GM6R2=Gm9R2121⇒m=3M242

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The acceleration due to gravity at Moon Surface is $\frac{g}{6}$ . If radius of Moon is $\frac{3 R}{11}$ mass of moon is $\frac{3 M}{x}$ Find ‘ $x$ ’ (where g is the acceleration due to gravity on earth surface, R is radius of earth, M is the mass of earth)

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answer is 242.

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Detailed Solution

$\frac{g}{6} = \frac{G m}{{(\frac{3 R}{11})}^{2}} \Rightarrow \frac{G M}{6 R^{2}} = \frac{G m}{\frac{9 R^{2}}{121}}$

$\Rightarrow m = \frac{3 M}{242}$

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