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The expression for the acceleration due to gravity $g$ on the surface of the Earth in terms of its mass $M$ and radius $R$ is:
A$g = \dfrac{GM}{R^2}$
B$g = \dfrac{GM}{R}$
C$g = \dfrac{GM^2}{R}$
D$g = \dfrac{GR}{M^2}$
Answer & Solution
Correct answer: A. $g = \dfrac{GM}{R^2}$
1. Gravitational force on a body: $F = \dfrac{GMm}{r^2}$.
2. By Newton's second law this force gives weight $F = mg$.
3. Equating, $mg = \dfrac{GMm}{r^2}$, so $g = \dfrac{GM}{r^2}$.
4. On the surface $r = R$, hence $g = \dfrac{GM}{R^2}$; the radius appears squared.
_Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 1 "Gravitation", p.17_
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