G Variation (depth)
For depth d inside Earth (uniform density) g_d ≈ g(1 - d/R). Depth where g halves?
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About This Question
- Subject
- physics
- Chapter
- gravitation
- Topic
- g variation (depth)
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
R/2
- Depth Formula: gd=gs(1−Rd), where gs is surface gravity.
- Condition: We want the gravity to be half of the surface value: gd=21gs.
- Equating: 21gs=gs(1−Rd).
- Solve for d:
- 21=1−Rd
- Rd=1−21=21
- d=2R.
- Conclusion: Halfway to the center of the Earth, gravity is half the surface value.
This medium difficulty physics question is from the chapter gravitation, covering the topic of g variation (depth). It appeared in the 2025 exam.
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