A parallel-plate capacitor is disconnected from a battery, and the plates are pulled a small distance farther apart. Does Q increase, decrease, or stay the same?

Q stay the same

Explanation:

Charging of capacitor is done by battery . If battery is disconnected , charging will stop . There will not be any discharging as plates are separate . So pulling the plates apart will not affect the charge lying on the capacitor . It will decrease its capacity and increase its potential , keeping its charge constant.

Before coming to the conclusion,first we have to know about the static and dynamic equilibrium.

As per Newton's first law ,a body continues to be at state of rest or of uniform motion along  a straight line as long as there is no external unbalanced force acting on it.

Hence if the net force is zero,the body  at rest will be at rest.This is called static equilibrium .Hence the condition for a body to be in static equilibrium is that sum of mechanical force is zero.

i.e

Again if the net force is zero,then velocity of the body won't be changed.Hence the acceleration of the body will be zero.This is called dynamic equilibrium where a body will move with uniform velocity  in the absence of net external force.

Hence if the net force is zero,then body will be both in static and dynamic equilibrium.

Hence the option  D  is right which  tells that a body in either state of equilibrium has no net force acting on it.