Final answer:
The free-fall acceleration on planet 2 is 9 m/s².
Step-by-step explanation:
To find the free-fall acceleration on planet 2, we can use the relationship between the radius and the mass of the planet and the free-fall acceleration. Since the radius of planet 2 is twice that of planet 1, and the mass of planet 2 is also twice that of planet 1, we can use the formula g = (G * M) / r², where G represents the gravitational constant, M represents the mass of the celestial body, and r represents the radius of the celestial body.
Let's assume the free-fall acceleration on planet 2 is a. Since the radius and mass of planet 2 are twice those of planet 1, we can write the following equation: a = (G * 2M) / (2r)². We can simplify this equation to a = (G * 2M) / 4r², which can be further simplified to a = (G * M) / 2r². This equation tells us that the free-fall acceleration on planet 2 is half that of planet 1. Therefore, the free-fall acceleration on planet 2 is 9 m/s².