The acceleration due to gravity on the surface of the moon is 1.62 $ms^{-2}$. The radius of the Moon is 1740 km. Find the mass of the moon.
Difficulty: Medium
Solution:
Acceleration due to gravity = $g_{m} = 1.62 ms^{-2}$
Radius of the moon = $R_{m}$ = 1740 km = $1740 \times1000$ m = $1.74 \times 10^{6} m$
Mass of moon = $M_{m}$ = ?
$g_{m}$ = $G M_{m}/〖R〗^{2}_m$
or
$M_{m}$ = $(\frac{gm\times〖R〗_{m})}{G}$
$M_{m}$ = $(\frac{1.62\times(1.74 \times10^{6}))^{2}}{(6.673 \times 10^{-11})}$
= $(\frac{1.62\times 3\times10^{12})}{(6.673\times 10^{-11})}$
$M_{m}$ = $7.35 \times 10^{22}$ kg
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