Final answer:
The gravitational acceleration on the surface of a planet with twice the mass of Earth but the same radius would be twice as much as Earth's gravity. This is because gravitational acceleration is directly proportional to the mass and inversely proportional to the square of the radius - since the radius has not changed, only mass, the gravity doubles.
Step-by-step explanation:
When considering a planet with twice the mass of Earth, but the same radius, the acceleration due to gravity on the surface of this planet can be found using the formula for gravitational force, which is Fgravity = (G * m1 * m2) / r^2, where m1 and m2 are the masses of the two objects, G is the gravitational constant, and r is the distance between the centers of the two masses. Since we are comparing the gravity of a planet with Earth, we can simplify the comparison by using the surface gravity on Earth (g) as a reference, which is approximately 9.8 m/s².
The acceleration due to gravity, g, is directly proportional to the mass of the planet and inversely proportional to the square of the radius of the planet. As the planet in question has twice the mass of Earth and the same radius, the gravitational acceleration at the surface would be twice as much as on Earth (g' = 2g), since the increase in mass directly doubles the force whereas the radius remains constant. There is no inverse square relationship since we are not changing the radius, only the mass.
Therefore, the correct answer to the question would be (d) twice as much as on Earth.