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Earth's mass is $6 \times 10^{24}$ kg and the Moon's is $7.4 \times 10^{22}$ kg, separated by $3.84 \times 10^8$ m. With $G = 6.7 \times 10^{-11}$ N m$^2$ kg$^{-2}$, the gravitational force between them is about:
A$2 \times 10^{18}$ N
B$2 \times 10^{20}$ N
C$7.4 \times 10^{20}$ N
D$2 \times 10^{22}$ N
Answer & Solution
Correct answer: B. $2 \times 10^{20}$ N
1. Use $F = \dfrac{G m_1 m_2}{r^2}$ with $r = 3.84\times10^8$ m (since $3.84\times10^5$ km $= 3.84\times10^8$ m).
2. Numerator $= 6.7\times10^{-11}\times6\times10^{24}\times7.4\times10^{22} = 2.975\times10^{37}$.
3. Denominator $r^2 = (3.84\times10^8)^2 = 1.475\times10^{17}$.
4. $F = \dfrac{2.975\times10^{37}}{1.475\times10^{17}} \approx 2\times10^{20}$ N.
5. Mis-converting km to m shifts the exponent and produces the trap options.
_Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 1 "Gravitation", p.24_
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