Final answer:
To maintain equilibrium and keep the object at rest, force Y must have a magnitude equal to x and must point upward, which counteracts the downward force X.
Step-by-step explanation:
The question addresses the concept of equilibrium in physics, where an object remains at rest when the net force acting on it is zero. When two forces, X and Y, act on an object at rest, with force X having a magnitude of x and acting downward, the magnitude and direction of Y must be such that it cancels out the effect of X.
For the object to remain at rest, force Y must have a magnitude equal to x and point in the upward direction (option a). This is because forces in equilibrium are equal in magnitude and opposite in direction (Newton's first law of motion).