Final answer:
The acceleration due to gravity (g) on Planet 2, which has twice the mass and radius of Planet 1, would be half of Planet 1's gravity, resulting in 7.5 m/s².
Step-by-step explanation:
The free-fall acceleration (g) at the surface of a planet is determined by the planet's mass (M) and radius (R) and can be calculated using the formula g = G*M/R², where G is the gravitational constant. For Planet 1, the free-fall acceleration is 15 m/s².
Given that the radius and the mass of Planet 2 are twice those of Planet 1, we would plug in values of 2M and 2R into the formula to find the acceleration due to gravity on Planet 2. Thus, g = G*(2M)/(2R)² = (G*M/R²) / 2 = 15 m/s² / 2 = 7.5 m/s². This shows that the acceleration due to gravity on Planet 2 would be half that of Planet 1, which is 7.5 m/s².