You obviously don’t need to write out the answer in such detail in a multiple-choice test, but it is worth doing it so that you can see exactly why the answer is (A). This question requires that you understand circular motion and are able to write down the forces and apply the equation F = ma, without getting confused by doubts about ‘centrifugal force’.
People often find circular motion hard to understand, and there are two confusions that crop up again and again. So it pays to remember these two principles:
- Centripetal acceleration is a geometric property of circular motion. That is, even in a world where there were no such thing as mass, or force, a point moving in a circle would still be accelerating towards the centre of the circle. It’s just because of the geometry of the situation. It is worth working out for yourself the centripetal acceleration of a point moving in a circle, without any mention of mass, just to ensure you remember this.
- If you find yourself thinking about ‘causality’, stop. In mechanics there is no such thing as causality: there are masses, forces and accelerations, and a law linking them together in an equation. So statements like “the object has inertia, which makes it want to go straight on and this causes it to exert a centrifugal force on the track” are a recipe for disaster.
So do what we have done in the question above: find the kinetic energy (and hence the velocity) of the puck in terms of its loss in potential energy, write down the forces on the puck, and the acceleration that the puck is undergoing, find a suitable direction to resolve the force and acceleration vectors, and apply F = ma.
Once you have done this, there is a trick that comes up very often in mechanics. For an object to stick to another object, there is a condition that they are pushing against each other with a force F, where F must be greater than or equal to zero. If the pushing force is less than zero, the objects won’t remain touching.