Question

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 becomeA) 1/2 of what it now is.B) 2 times what it now is.C) 1/4 of what it now is.D) the same as it now is.E) 4 times what it now is.

Answer 1

Answer:

B) 2 times what it now is

Explanation:

The acceleration due to gravity at the surface of the Earth is given by

$g=\frac{GM}{R^2}$

where

G is the gravitational constant

M is the mass of the Earth

R is the Earth's radius

In this problem, the mass of the Earth is doubled:

M' = 2M

while the radius remains the same:

R' = R

so the new acceleration due to gravity would be

$g'=\frac{GM'}{R'^2}=\frac{G(2M)}{R^2}=2\frac{GM}{R^2}=2g$

so, the acceleration due to gravity would become twice the current value.

Note also that the value of g does not depend on the mass of the objects involved.