A question about central forces

Question

Will a force pointing towards a fixed point but having constant magnitude (and not depending on the distance from fixed point) be a central force?

Answer 1

We will have to start with the definition of central force.

In classical mechanics, a central force on an object is a force whose magnitude only depends on the distance $r$ of the object from the origin, and is directed along the line joining them.

In short, the forces acting upon the line joining the centers of two bodies are called central forces.

The stress is on the distance of the body from the origin, and the force has to be directed along the line joining the origin and the body.

So, in your example, the force is a central force.

Examples of central force are Coloumbic force, and Gravitational force.

Later on, you might encounter a term, central potential, which is simply the potential depending on the distance of a body from the origin.

Anything central means that only depends on distance from origin.

In the above picture, the distance of the body at P from O is $r$. As the force $F_{att} $ acts along the line joining the body and the origin, that is the position vector, the force is a central force.