If a planet has a mass twice that of Earth and a radius four times that of Earth,the ratio of the acceleration due to gravity on the planet to that on Earth is
A)1/8
B)1/2
C)1/16
D)2/1
E)12/1

Question

Quizplus · Accepted Answer

The acceleration due to gravity is given by $ g = \frac{GM}{R^2} $. If the mass is twice Earth's (2M) and the radius is four times Earth's (4R), then the gravity on the planet is $ \frac{G(2M)}{(4R)^2} = \frac{2GM}{16R^2} = \frac{1}{8} \times \frac{GM}{R^2} $, which is 1/8 of Earth's gravity.

If a Planet Has a Mass Twice That of Earth