Variation Of G With Height
At small height h ≪ R above Earth, g decreases approximately by factor?
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About This Question
- Subject
- physics
- Chapter
- gravitation
- Topic
- variation of g with height
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
1 - 2h/R
- General Case: Acceleration at height h is gh=(R+h)2GM.
- Relation to Surface g: gs=R2GM. So, gh=gs(R+h)2R2=gs(1+Rh)−2.
- Approximation: For h≪R, we use the binomial expansion (1+x)n≈1+nx. Here x=h/R and n=−2.
- Result: gh≈gs(1−R2h).
- Impact: Gravity decreases as we go higher; the decrease is roughly linear for small heights.
This hard difficulty physics question is from the chapter gravitation, covering the topic of variation of g with height. It appeared in the 2025 exam.
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