If the mass and radius of Mars to Earth are 11% and 53% respectively,calculate the ratio of the escape velocity of Earth divided by that of Mars.
A)4.8
B)2.2
C)0.5
D)6.6
E)1.6

Question

Quizplus · Accepted Answer

The escape velocity of a planet is given by:

Ve = sqrt((2GM)/r)

where G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet.

Since we want to find the ratio of the escape velocity of Earth to that of Mars, we can write:

Ve(earth) / Ve(mars) = sqrt((2G*M_earth)/r_earth) / sqrt((2G*M_mars)/r_mars)

Simplifying this expression using the given values for the mass and radius ratios, we get:

Ve(earth) / Ve(mars) = sqrt((M_earth / M_mars) * (r_mars / r_earth))
                      = sqrt((1/0.11) * (0.53/1))
                      = sqrt(4.818)
                      = 2.2

Therefore, the ratio of the escape velocity of Earth to that of Mars is 2.2, which corresponds to choice (B).

If the Mass and Radius of Mars to Earth Are