Short Answer
√(2GM/R) is the best answer.
This concept lives inside the mechanics toolkit: forces, motion, energy, momentum, and rotation. The safest way to solve it is to name the governing law first, then connect the variables in units you trust.
Setting ½mv² = GMm/R and solving gives v_esc = √(2GM/R).
Why This Answer Is Correct
This is a Medium-level question in Classical Mechanics. The prompt is really testing whether you can connect the concept to its defining physical relationship instead of picking a nearby-but-wrong term.
Mechanics questions usually become easier once you identify whether the problem is about force balance, kinematics, energy, or conservation.
Choices At A Glance
- A. √(GM/R)
- B. √(2GM/R)
- C. 2GM/R²
- D. GM/R²
When similar options appear on an exam, eliminate the ones that break the core law, use the wrong units, or confuse a definition with a consequence.
Topic Snapshot
Topic: Classical Mechanics
Difficulty: Medium
Best next move: Re-state the governing law in your own words, then solve one more example from the same topic before moving on.