Answer to Question #121141 in Classical Mechanics for Lizwi

Question

Does a planet that has a greater mass than Earth necessarily have a greater acceleration due to gravity near its surface? (Saturn, for example, has about a hundred times the mass of Earth.)
1 : Yes
2 : No
3 : More information is needed to say

Answer 1

No.

Reason:

According to newton's law of gravitation

$$F_G=G\frac{M_pm}{r^2}\\ \implies a_{gravity}=\frac{F_G}{m}=G\frac{M_p}{r^2}\\$$

where, $M_p$ is mass of planet and $r$ is distance between planet's center to particle of mass m lies on it's surface.

Thus , If a planet has lower density than earth i.e mass is higher and $r$ is also very higher compared to earth's radius ,then above statement is not true.