The same event interpreted by different observers While my physics teacher was explaining pseudo forces to us he gave the following example :

An elevator is accelerating upwards. In it there is a bob strung up by a rope. There are two observers, A in the elevator and B outside of the elevator, on the ground and not accelerating.
Due to the action of gravity and the lift's acceleration the rope breaks and the bob falls. Does it do so at the same time for the two observers?

The falling of the bob will be registered only when an observer sees a change in its position. This will happen earlier for observer A in the elevator compared with observer B outside.
Question: At a particular time instant, is it possible for the rope (which holds the bob) to be both broken and taut for different observers?
 A: Yes, the rope breaks at the same time for both observers unless the elevator is moving at an appreciable fraction of the speed of light with respect to the observer outside of the elevator. Whether or not a person notices the rope breaking immediately or if one person reacts faster is a psychology question.
A: I think your question is rather confused, perhaps because your teacher was using the example to illustrate something about pseudo-forces, whereas you are trying to use the same example to ask about something entirely different. For your purpose, what is the significance of the acceleration (or constant velocity) of the lift?
The key phrase in your question is "at a particular time instant." The difficulty is, what does this phrase mean? 
If it means, "Does the light which carries the information about the rope breaking reach A and B simultaneously?" then the answer is obviously "No." As you observe, it reaches A first. Even if their clocks are synchronized, A & B will agree that, for example, the rope breaks when the clock in the elevator reads 1pm, and that the light from this event reaches B when his clock reads 2pm. 
If the phrase means something else, then what is that? 
The problem is that there is no universal clock built into the fabric of space, so whether a single event happens "at the same instant of time" for two different observers who are separated by some distance is meaningless.
