Here is what I was thinking:
Case (1):If a small force not enough to break the string is applied, all parts of the system receive this force at some instant because of the tension and Newton's third law. But eventually the force is felt at $A$.
i.e: a force applied on a small part of the string causes an instantaneous acceleration on the small part which puts a force on the adjacent part above it.The adjacent part applies the same force so that the part which experienced the force first does not move.
This goes as a chain reaction and eventually the force is propagated to the top at point $A$.
Since the part $AB$ has to support the block,it also experiences a force of $9.8N$.
So if a force is applied to the string and gradually increased, a part in $AB$ is more likely to break.
=> Is everything in the above case(1) that I have said, correct?
Case(2): Now a very large impulsive force is applied to the system which is enough to break the string.
$BC$ will definitely break. But the question is, will $AB$ also break?
I think that a force just infinitesimally smaller than the force required to break the string would propagate onto the string $AB$ just before $BC$ breaks.
However since the string $AB$ also experiences the weight of the block, which is non zero, the string must break as well.
So both parts $AB$ and $BC$ will break.
=> Is this right?
Edit: what is the condition for both AB and BC to break?