The mass of the Moon is $7.4 \times 10 ^ { 22 } \mathrm {~kg}$
its radius is $1.74 \times 10 ^ { 3 } \mathrm {~km}$
and it has no atmosphere. What is the acceleration due to gravity at the surface of the Moon? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$
A) $2.8 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s } ^ { 2 }$
B) $4.9 \mathrm {~m} / \mathrm { s } ^ { 2 }$
C) $1.6 \mathrm {~m} / \mathrm { s } ^ { 2 }$
D) $0.80 \mathrm {~m} / \mathrm { s } ^ { 2 }$
E) $9.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$

Question

Quizplus · Accepted Answer

The acceleration due to gravity at the surface of a celestial body can be calculated using the formula $g = \frac{GM}{r^2}$, where $G$ is the gravitational constant, $M$ is the mass of the body, and $r$ is its radius. Substituting the given values: $g = \frac{6.67 \times 10^{-11} \mathrm{N\cdot m^2/kg^2} \times 7.4 \times 10^{22} \mathrm{kg}}{(1.74 \times 10^6 \mathrm{m})^2}$, we find $g \approx 1.6 \mathrm{m/s^2}$.

The Mass of the Moon Is 7.4×1022 kg7.4 \times 10 ^ { 22 } \mathrm {~kg}7.4×1022 kg

The Mass of the Moon Is $7.4 \times 10 ^ { 22 } \mathrm {~kg}$