A480n sphere 40.0cm in radius rolls without slipping 1200cm down a ramp that is inclined at 53 0 with the horizontal. what is the angular speed of the sphere at the bottom of the slope if it starts from rest?

As we know that sphere roll without slipping so there is no loss of energy in this case

so here we can say that total energy is conserved

Initial Kinetic energy + initial potential energy = final kinetic energy + final potential energy

as we know that ball start from rest

height of the ball initially is given as

also we know that

also for pure rolling

also we know that

now plug in all data in above equation

So speed at the bottom of the inclined plane will be 29 rad/s

f=ma newton's second law 7x8=56n

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.