本题目来源于试卷: 2012美国US F=MA物理竞赛，类别为 美国F=MA物理竞赛
[单选题]
A uniform spherical m a6, c*.kroprplav:*n5(o sjc* mx6 4 z;ithza5nyr ir4bnet has radius $R$ and the acceleration due to gravity at its surface is $g$. What is the escape velocity of a particle from the planet's surface?
A. $\frac{1}{2}\sqrt{gR}$
B. $\sqrt{gR}$
C. $\sqrt{2gR}$
D. $2\sqrt{gR}$
E. The escape velocity cannot be expressed in terms of $g$ and $R$ alone.
参考答案: C
本题详细解析:
Escape velocity $v_e$ is the speed needed so that the total energy $E = KE + PE_g = 0$.
$E = \frac{1}{2}mv_e^2 - \frac{GMm}{R} = 0$
$\frac{1}{2}mv_e^2 = \frac{GMm}{R} \implies v_e = \sqrt{\frac{2GM}{R}}$.
We also know that at the surface, $g = \frac{GM}{R^2}$, which means $GM = gR^2$.
Substitute this into the $v_e$ equation: $v_e = \sqrt{\frac{2(gR^2)}{R}} = \sqrt{2gR}$.
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