114 學年度臺灣大學轉學生招生考試｜第 55 題
普通物理學(A)
- 11 km/s
- 22 km/s
- 5.5 km/s
- 44 km/s
- 2.75 km/s
提示
Write the escape-velocity formula from energy conservation and notice which quantities it actually contains. Does the mass of the escaping object appear?
正確答案
正解：A
詳解
A. (A) 11 km/s — correct. Escape velocity comes from ½mv² = GMm/R, and the object's mass m cancels: v_esc = √(2GM/R). It depends only on the planet's mass and radius, so any object — 50 kg or 100 kg — escapes at the same ~11 km/s.
B. (B) 22 km/s — incorrect. This doubles the speed, as if escape velocity scaled with the object's mass; it does not.
C. (C) 5.5 km/s — incorrect. This halves the speed, the common mistake of assuming a lighter object escapes more easily. Mass cancels out.
D. (D) 44 km/s — incorrect. Quadrupling the speed has no physical basis; escape velocity is independent of the escaping mass.
E. (E) 2.75 km/s — incorrect. Dividing by four also wrongly assumes a dependence on the object's mass.
