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Given the Moon's mass $7.34 \times 10^{22}$ kg, radius $1.74 \times 10^6$ m and $G = 6.67 \times 10^{-11}$ N m$^2$/kg$^2$, the escape velocity from the Moon is about:
A0.24 km/s
B11.2 km/s
C5.62 km/s
D2.37 km/s
Answer & Solution
Correct answer: D. 2.37 km/s
1. Use $v_{esc} = \sqrt{\dfrac{2GM}{R}}$.
2. Numerator $2GM = 2\times6.67\times10^{-11}\times7.34\times10^{22} = 9.79\times10^{12}$.
3. Divide by $R = 1.74\times10^6$: $\dfrac{9.79\times10^{12}}{1.74\times10^6} = 5.63\times10^6$.
4. $v_{esc} = \sqrt{5.63\times10^6} \approx 2.37\times10^3$ m/s $= 2.37$ km/s.
5. 11.2 km/s is the Earth's escape velocity, so it is the trap.
_Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 1 "Gravitation", p.23_
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