$\begin{array} { | c | c | c | c | c | }
\hline & \text { Mass } & \text { Radius } & \text { Orbital radius } & \text { Orbital period } \
\hline \text { Moon A } & 4.0 \times 10 ^ { 20 } \mathrm {~kg} & \text { unknown } & 2.0 \times 10 ^ { 8 } \mathrm {~m} & 4.0 \times 10 ^ { 6 } \mathrm {~s} \
\hline \text { Moon B } & 1.5 \times 10 ^ { 20 } \mathrm {~kg} & 2.0 \times 10 ^ { 5 } \mathrm {~m} & 3.0 \times 10 ^ { 8 } \mathrm {~m} & \text { unknown } \
\hline
\end{array}$
Mithra is an unknown planet that has two airless moons, A and B , in circular orbits around it. The table summarizes the hypothetical data about these moons. If you dropped a laser at the surface of Moon B, at what rate would it accelerate toward the ground? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$
A) $0.25 \mathrm {~m} / \mathrm { s } ^ { 2 }$
B) $0.10 \mathrm {~m} / \mathrm { s } ^ { 2 }$
C) $0.30 \mathrm {~m} / \mathrm { s } ^ { 2 }$
D) $0.15 \mathrm {~m} / \mathrm { s } ^ { 2 }$
E) $0.20 \mathrm {~m} / \mathrm { s } ^ { 2 }$

Question

$\begin{array} { | c | c | c | c | c | } 
\hline & \text { Mass } & \text { Radius } & \text { Orbital radius } & \text { Orbital period } \
\hline \text { Moon A } & 4.0 \times 10 ^ { 20 } \mathrm {~kg} & \text { unknown } & 2.0 \times 10 ^ { 8 } \mathrm {~m} & 4.0 \times 10 ^ { 6 } \mathrm {~s} \
\hline \text { Moon B } & 1.5 \times 10 ^ { 20 } \mathrm {~kg} & 2.0 \times 10 ^ { 5 } \mathrm {~m} & 3.0 \times 10 ^ { 8 } \mathrm {~m} & \text { unknown } \
\hline
\end{array}$
Mithra is an unknown planet that has two airless moons,  A  and  B , in circular orbits around it. The table summarizes the hypothetical data about these moons. If you dropped a laser at the surface of Moon B, at what rate would it accelerate toward the ground? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$
A) $0.25 \mathrm {~m} / \mathrm { s } ^ { 2 }$
B) $0.10 \mathrm {~m} / \mathrm { s } ^ { 2 }$
C) $0.30 \mathrm {~m} / \mathrm { s } ^ { 2 }$
D) $0.15 \mathrm {~m} / \mathrm { s } ^ { 2 }$
E) $0.20 \mathrm {~m} / \mathrm { s } ^ { 2 }$

Quizplus · Accepted Answer

The acceleration due to gravity on the surface of Moon B is:$$g = \frac{Gm}{r^2}$$where G is the gravitational constant, m is the mass of Moon B, and r is the radius of Moon B.Plugging in the given values, we get:$$g = \frac{(6.67 	imes 10^{-11} \mathrm{~N} \cdot \mathrm{ m }^ { 2 } / \mathrm { kg } ^ { 2 })(1.5 	imes 10 ^ { 20 } \mathrm {~kg})}{(2.0 	imes 10 ^ { 5 } \mathrm {~m})^2} = 0.25 \mathrm {~m} / \mathrm { s } ^ { 2 }$$Therefore, the acceleration due to gravity on the surface of Moon B is 0.25 m/s^2.

Mithra Is an Unknown Planet That Has Two Airless Moons