CollegeBoard SAT Physics Study Guide PT1 Q74

CollegeBoard's Book

74) We want to find the ratio between the accelerations of gravity for the two planets. For this problem, we need to know the two formulas for gravitational force.

Where F is force, m is mass of object, a is acceleration due to gravity, G is gravitational constant, M is mass of planet, r is distance between planet and object

After this, we can equation these equations together.

Where F is force, m is mass of object, a is acceleration due to gravity, G is gravitational constant, M is mass of planet, r is distance between planet and object

At this point, the only variables we need to compare, are the acceleration due to gravity and the radius. We can rewrite the above equation into a proportion.

Where a is acceleration due to gravity and r is radius

Since the problem states the radius of Planet Y is 3 times of Planet X we can replace r with 3r and bring out the constant.

Where a is acceleration due to gravity and r is radius

In this form, it is noticeable that the acceleration due to gravity of Plant Y will be 1/9 of that of Planet X.

Answer: E