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Using $g = \dfrac{GM}{R^2}$ with $G = 6.67 \times 10^{-11}$ N m$^2$/kg$^2$, $M = 6 \times 10^{24}$ kg and $R = 6.4 \times 10^6$ m, the value of $g$ at the Earth's surface is about:
A9.77 m/s$^2$
B98.0 m/s$^2$
C1.56 m/s$^2$
D0.98 m/s$^2$
Answer & Solution
Correct answer: A. 9.77 m/s$^2$
1. Use $g = \dfrac{GM}{R^2}$.
2. Numerator $= 6.67\times10^{-11}\times6\times10^{24} = 4.00\times10^{14}$.
3. Denominator $R^2 = (6.4\times10^6)^2 = 4.096\times10^{13}$.
4. $g = \dfrac{4.00\times10^{14}}{4.096\times10^{13}} \approx 9.77$ m/s$^2$.
5. The other options misplace the decimal/power and are wrong.
_Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 1 "Gravitation", p.17_
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