If the mass of the earth and all objects on it were suddenly doubled,but the size remained the same,the acceleration due to gravity at the surface would become
A) 4 times what it now is.
B) 2 times what it now is.
C) the same as it now is.
D) 1/2 of what it now is.
E) 1/4 of what it now is.

Question

Quizplus · Accepted Answer

The acceleration due to gravity is directly proportional to the mass of the Earth. If the mass doubles, the acceleration due to gravity also doubles, according to the formula $g = \frac{G M}{r^2}$, where $G$ is the gravitational constant, $M$ is the mass of the Earth, and $r$ is the radius of the Earth. Since only the mass $M$ is doubled and $r$ remains the same, $g$ would double.

If the Mass of the Earth and All Objects on It