A particular asymptotic giant branch star has approximately the same mass as the Sun but 100 times its radius. Compared to the Sun, what is the escape velocity from that star?
A) 0.01 times that of the Sun
B) 0.1 times that of the Sun
C) the same as that of the Sun
D) 10 times that of the Sun
E) 100 times that of the Sun

Question

Quizplus · Accepted Answer

The escape velocity is given by the equation v=sqrt(2GM/R), where G is the gravitational constant, M is the mass of the star and R is its radius. Since the mass of the star is the same as the Sun, we can assume that G is the same for both stars. However, the radius of the star is 100 times that of the Sun, leading to a much lower escape velocity. Plugging in the values, we get v = sqrt(2GM/100R) = 0.1sqrt(2GM/R), which is 0.1 times the escape velocity of the Sun. Therefore, the answer is B.

A Particular Asymptotic Giant Branch Star Has Approximately the Same