Working with gravitational force - calculation of the ratio of the radii of 2 planets

The weight of a object is the same on two different planets. The mass of planet A is only sixty percent that of planet B. Find ra/rb, which is the ratio of the radii of the planets.

Centripetal Force

In a skating stunt known as "crak-the-whip," a number of skaters hold hands and form a straight line. They try to skate so that the line rotates about the skater at one end, who acts as the pivot. The skater farthest out has a mass of 80.0 kg and is 6.10 m from the pivot. He is skating at a speed of 6.80 m/s. Determine the magnitude of the centripetal force that acts on him.

Bnaked Curves

On a banked race track, the smallest circular path on which cars can move has a radius of 112 m, while the largest has a radius of 165 m. The height of the outer wall is 18 m. Find (a) the smallest (b) the largest speed at which cars can move on this track without relying on friction.

Apparent Weightlessness and artificial gravity

The moon orbits the earth at a distance of 3.85 x 10^8 m. Assume that this distance is between the centers of the earth and the moon and that the mass of the earth is 5.98 x 10^24 kg. Find the period for the moons motion around the earth. Express the answer in days and compare it to the length of a month.

Vertical Circular motion

A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to twice her weight as she goes through the dip. If r + 20.0 m, how fast is the roller coaster traveling at the bottom of the dip?