Titan, a satellite of Saturn, has a mean orbital radius of 1.22 × 10⁹ m. The orbital period of Titan is 15.95 days. Hyperion, another satellite of Saturn, orbits at a mean radius of 1.48 × 10⁹ m. Estimate the orbital period of Hyperion.

A box of mass 8.0 kg slides at a speed of 10 ms⁻¹ across a smooth level floor before it encounters a rough patch of length 3.0 m. The frictional force on the box due to this part of the floor is 70 N. What is the speed of the box when it leaves this rough surface? What length of the rough surface would bring the box completely to rest?

A girl is sitting with her dog at the left end of a boat of length 10.0 m. The mass of th girl, her dog and the boat are 60.0 kg, 30.0 kg and 100.0 kg respectively. The boat is at rest in the middle of the lake. Calculate the centre of mass of the system. If the dog moves to the other end of the boat, the girl staying at the same place, how far and in what direction does the boat move?

A horizontal rod with a mass of 10 kg and length 12 m is hinged to a wall at one end
and supported by a cable which makes an angle of 30º with the rod at its other end.
Calculate the tension in the cable and the force exerted by the hinge.

A crate of mass 30.0 kg is pulled by a force of 180 N up an inclined plane which makes an angle of 30º with the horizon. The coefficient of kinetic friction between the plane and the crate is μ_k = 0.225. If the crates starts from rest, calculate its speed after it has been pulled 15.0 m. Draw the free body diagram.

A child of mass 50 kg is standing on the edge of a merry go round of mass 250 kg and radius 3.0 m which is rotating with an angular velocity of 3.0 rad s⁻¹. The child then starts walking towards the centre of the merry go round. What will be the final angular velocity of the merry go round when the child reaches the centre?

A ball having a mass of 0.5 kg is moving towards the east with a speed of 8.0 ms^-1. After being hit by a bat it changes its direction and starts moving towards the north with a speed of 6.0 ms⁻¹. If the time of impact is 0.1 s, calculate the impulse and average force acting on the ball.