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 become.

Answer 1

When the mass of Earth doubles, acceleration due to gravity doubles as well.

Acceleration due to gravity

Apply Newton's second law of motion;

F = mg --- (1)

where;

• m is mass of the object
• g is acceleration due to gravity

F = GmM/R²  --- (2)

where;

• M is mass of Earth
• R is radius of Earth

Solve (1) and (2)

mg =  GmM/R²

g = GM/R²

when the mass of Earth doubles, acceleration due to gravity becomes;

g' = G(2M)/R²

g' = 2(GM/R²)

g' = 2g

Thus, when the mass of Earth doubles, acceleration due to gravity doubles as well.

Learn more about acceleration due to gravity here: brainly.com/question/88039

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