The answer is (c) decreases.
The idea behind this problem is that Earth's roration produces a centripetal acceleration, which is directed towards the center of rotation, that reduces the gravitational acceleration,
This centripetal acceleration is defined by the equation
The force that creates this centripetal acceleration is called the centripetal force and is pointed towards the center of ration as well.
Now, an object that is in a rotating reference frame, i.e. a reference frame that is rotating with the system, will be acted upon by the centrifugal force.
This "force" (it is not a force per se) points outwards from the center of rotation and actually replaces the centripetal force.
This means that, for a person that's rotating at the equator, this centifugal force will actually oppose gravity.
This means that the weight of the person at the equator will actually be
For future reference,
As you can see, the magnitude of
As a conclusion, the faster the Earth spins, the lower