If a planet has the same mass as the earth, but has twice the radius, how does the surface gravity, g, compare to g on the surface of the earth

The surface gravity g of the planet is 1/4 of the surface gravity on earth.

Explanation:

Surface gravity is given by the following formula:

So the gravity of both the earth and the planet is written in terms of their own radius, so we get:

The problem tells us the radius of the planet is twice that of the radius on earth, so:

If we substituted that into the gravity of the planet equation we would end up with the following formula:

Which yields:

So we can now compare the two gravities:

When simplifying the ratio we end up with:

So the gravity acceleration on the surface of the planet is 1/4 of that on the surface of Earth.

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.