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.

B) 2 times what it now is

Explanation:

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

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

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.

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