A55kg skater spins at 12 m/s while carving a circle on the ice that has a radius of 6.0m. what net force must act on the skater to keep her in the circular path?

The force counteracting the centrifugal force must be 1320N. The net force acting in the radial direction will thus be 0. (see comment below)

Explanation:

The force acting on the skater skating on a circular path is the centrifugal force. For the skater to stay on that path the blades must ensure sufficient "edge" to enact a counterforce of same magnitude but direction opposite to the centrifugal force.

The centrifugal force formula for this setting is as follows:

with m the mass, v the speed, and r the radius. Using values we are given, the force amounts to:

Comment:

I may be misunderstanding the question. The problem is likely asking for the force counteracting the centrifugal force, however, they use the term "net force" which I consider to be the result of adding the centrifugal and the force exerted on the skates' edges. That sum (in the radial direction) should be 0 if the skater is to stay in the path. You may be a better judge knowing your teacher.

As a side comment (opinion): the term "spin" implies rotation around own axis. So, in this context it is quite a misnomer. The skater surely is not spinning around her own axis while carving a circle as written in this problem.

i believe it is b. what was the cause of the big bang

hope this !

increase masses, decrease separation