Answer
a) is correct.
Work Step by Step
An isolated system does not have any external forces acting on the objects in the system and affecting their motion. Let's examine each situation.
1) A ball falls because of gravitational force. Because the system is only the ball, gravitational force is external to the system, so this system is not an isolated system.
2) In this case, gravitation is an internal force in the system of the ball and the earth, so b) is an isolated system.
3) A billiard ball, when collided with another ball, has a force acted on it from the other billiard ball. Because we limit the system to only the moving ball, the mentioned force is external to the system, so this is not an isolated system.
4) A car slides to a halt thanks to kinetic friction. Because the system is only the car, kinetic friction is an external force, so d) is not an isolated system.
5) The space probe is not under the influence of any forces in this case, so it is indeed an isolated system.
