An object is suspended by two ideal (taut) ropes connected to the ceiling and the wall, as shown. How does the tension, T, in the rope attached to the ceiling compare to the weight of the object?

The tension on the rope must be equal to the weight of the objects that are attached
The tension force is the force that acts on the rope a it is attached to a point in order to hold a mass in place. The tension force is responsible for the tautness of the rope.
As such the tension on the rope must be equal to the weight of the objects that are attached thus; T=w=mg.
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