Question

Planet X has DOUBLE the MASS of Earth and has a radius that is DOUBLE the Earth’s radius. The acceleration due to gravity on the surface of Planet X must be _____________.

A. 2g
B. 4g
C. g/2
D. g

Answer 1

The acceleration due to gravity on Planet X, which has double the mass and double the radius of Earth, is the same as Earth's, which is represented by D. g.

Step-by-step explanation:

The student has asked about the acceleration due to gravity on a hypothetical Planet X that has double the mass and double the radius of Earth. The acceleration due to gravity (g) on a planet is calculated using the formula g = (G * M) / r^2, where G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet. For Planet X, M is 2 times Earth's mass and r is 2 times Earth's radius. Plugging these values into the formula, we get g for Planet X = (G * 2M) / (2r)^2 = (G * 2M) / (4r^2) = (1/2) * (G * M) / r^2. This shows that Planet X has the same acceleration due to gravity as Earth, so the correct answer is D. g.