State whether the following statements are true or false:
$(a)$ $A$ necessary condition for equilibrium is that the acceleration must be zero.
$(b)$ Centripetal force is always in the opposite direction of centrifugal force.
$(c)$ $A$ man is at rest on a perfectly smooth ice surface in the middle of a pond. He can reach the shore by using Newton's first law.
$(d)$ An object is in equilibrium only if it is at rest.

(A) True: Equilibrium implies the net force is zero,which means acceleration $a = 0$ according to Newton's second law.
$(b)$ True: Centripetal force acts towards the center,while centrifugal force (a pseudo-force in a rotating frame) acts away from the center.
$(c)$ False: On a perfectly smooth (frictionless) surface,a man cannot exert a horizontal force to change his state of motion. Newton's first law states an object at rest remains at rest unless acted upon by an external force.
$(d)$ False: An object moving with constant velocity is also in equilibrium (dynamic equilibrium),as its acceleration is zero.