The mass and radius of the planet Venus are 81% and 95% that of Earth,respectively.How much faster or slower (as a percentage)is the escape velocity from Venus compared to that of Earth?
A)8% slower
B)8% faster
C)12% slower
D)12% faster
E)17% slower

Question

Quizplus · Accepted Answer

The escape velocity $v$ from a planet is given by the formula $v = \sqrt{\frac{2GM}{r}}$, where $G$ is the gravitational constant, $M$ is the mass of the planet, and $r$ is the radius of the planet. Since the mass of Venus is 81% that of Earth and its radius is 95% that of Earth, the escape velocity from Venus, relative to Earth, changes by a factor of $\sqrt{\frac{0.81}{0.95}}$, which is approximately 0.92, indicating that the escape velocity from Venus is 8% slower than that from Earth.

The Mass and Radius of the Planet Venus Are 81