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Gravitational Potential Energy
Gravitational potential energy is the energy associated with the position of masses in a gravitational field. For masses `M` and `m` separated by `r`: U = −GMm/r when zero energy is chosen at infinity.
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Gravitational Potential Energy
What is it?
Gravitational potential energy is the energy associated with the position of masses in a gravitational field. For masses `M` and `m` separated by `r`: U = −GMm/r when zero energy is chosen at infinity.
In simple words
- Bound gravitational systems have negative U relative to infinity.
Recommended for Class 12
Full school-level explanation
Gravitational potential energy is the energy associated with the position of masses in a gravitational field. For masses `M` and `m` separated by `r`: U = −GMm/r when zero energy is chosen at infinity.
Why Negative?
Since: V = Um and: V = −GM/r therefore: U = −GMm/r At infinity: U = 0 At any finite distance: U < 0 A bound object must gain energy to reach infinity with zero final speed.
Change in Potential Energy
Moving from 0 to 1: **ΔU = U₂ − U₁** **ΔU = −GMm/r₂ + GMm/r₁**
Formula / Key Relation
**U = −GMm/r**
Remember
- U = 0
- U < 0
- ΔU = U₂ − U₁
- ΔU = −GMm/r₂ + GMm/r₁
- U = −GMm/r
Deeper understanding
Go deeper on Gravitational Potential Energy: connect the definition to reasons, relationships, exceptions, and exam wording.
Common mistakes
Exam focus
Near surface small h
Exam focus
Quick revision
- U = 0
- U < 0
- ΔU = U₂ − U₁
- ΔU = −GMm/r₂ + GMm/r₁
- Why Negative?: Since: **V = Um** and: **V = −GM/r** therefore: **U = −GMm/r** At infinity: **U = 0** At an
- Change in Potential Energy: Moving from `r₁` to `r₂`: ΔU = U₂ − U₁ ΔU = −GMm/r₂ + GMm/r₁
For long answers on Gravitational Potential Energy: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- U = 0
- U < 0
- ΔU = U₂ − U₁
- ΔU = −GMm/r₂ + GMm/r₁
Important formulas
- U = 0
- U < 0
- ΔU = U₂ − U₁
Common exam traps
- Do not use `mgh` for situations extending over distances comparable to Earth’s radius.
- `mgh` is a near-surface approximation.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Do not use `mgh` for situations extending over distances comparable to Earth’s radius.
- Mistake
`mgh` is a near-surface approximation.
- Mistake
Do not use `mgh` for situations extending over distances comparable to Earth’s radius.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
U = 0
U < 0
ΔU = U₂ − U₁
ΔU = −GMm/r₂ + GMm/r₁
Gravitational potential energy is the energy associated with the position of masses in a gravitational field. For masses `M` and `m` separated by `r`: **U
U = 0
- Definition
- Gravitational potential energy is the energy associated with the position of masses in a gravitational field. For masses `M` and `m` separated by `r`: **U
- Formula
- U = 0
- Critical warning
- Do not use `mgh` for situations extending over distances comparable to Earth’s radius.
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Exam Practice
Define
Q1. Define Gravitational Potential Energy.
Explain
Q2. Explain: Why Negative?.
Example
Q3. Give one clear example of Gravitational Potential Energy and say why it fits.
Mistake
Q4. State one common mistake students make about Gravitational Potential Energy.
Exam note
Q5. Write a short exam note on Gravitational Potential Energy: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.