Block hanging with a string and being pulled downwards
with a similar string  

A block of a mass 1 kg is hanging from the ceiling by a string. It is pulled from below through another string with a force F. Both strings are identical.

Block hanging with a string and being pulled downwards
with a similar string

If the force F is gradually increased, which string will snap first ? What is the difference between the tensions in the two strings, if any ?

Free-body diagram of the block

Free-body diagram of the block

Free-body diagram of the block

When the block is in equilibrium,
T₁ = F+9.81 N
T₂ = F

If F is increased T1 gets increased. Therefore, when the tension in the upper string increases beyond the strength of the string , it will snap first.