Question

For moon, $g=1.67m{s}^{-2}$ and $R=1.74\times {10}^{6}m$.
The Moon's mass is ___ $\times {10}^{22}kg$.

• A. 7.6

Answer 1

The correct option is A 7.6
Given:
The acceleration due to gravity of the Moon, ${\text{g}}_{\text{M}}=1.67\text{m}{\text{s}}^{-2}$
The radius of the Moon, ${\text{R}}_{\text{M}}=1.74\times {10}^6\text{m}$

Let ${\text{m}}_{\text{M}}$ be the mass of the Moon

The acceleration due to gravity is:
${\text{g}}_{\text{M}}=\frac{\text{G}{\text{m}}_{\text{M}}}{{\text{R}}_{\text{M}}^2}$
${\text{m}}_{\text{M}}=\frac{{\text{g}}_{\text{M}}{\text{R}}_{\text{M}}^2}{\text{G}}$
${\text{m}}_{\text{M}}=\frac{1.67\times (1.74\times {10}^6{)}^2}{6.67\times {10}^{-11}}$
${\text{m}}_{\text{M}}\approx 7.6\times {10}^{22}\text{kg}$