Acceleration Due To Gravity

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Value of g at height h above Earth (R radius) approximately is:

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g (1 - 2h/R)

$g (R / (R + h))^{2}$

g (R+h)/R

$g (R / (R - h))^{2}$

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Subject: physics
Chapter: gravitation
Topic: acceleration due to gravity
Difficulty: Medium
Year: 2025

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Correct Answer:

$g (R / (R + h))^{2}$

The acceleration due to gravity ( $g$ ) at the surface is $g = \frac{GM}{R ^{2}}$ .

At a height $h$ above the surface, the distance from the center is $(R + h)$ .
The value $g_{h} = \frac{GM}{( R + h ) ^{2}}$ .
Taking the ratio: $\frac{g _{h}}{g} = \frac{R ^{2}}{( R + h ) ^{2}} = (\frac{R}{R + h})^{2}$ .
For $h ≪ R$ , this simplifies using binomial expansion to $g_{h} \approx g (1 - \frac{2 h}{R})$ .

This medium difficulty physics question is from the chapter gravitation, covering the topic of acceleration due to gravity. It appeared in the 2025 exam.

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Acceleration Due To Gravity

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