Yes, while the pen at rest the string provide force on pen this force is called a tension force.

this illustration will help you to understand how tension force show on the hanging pen supporting by the string.

| --> string
! -->pen

the string act as a supplied force of pen, so if you cut the string with scissor the pen fall in what direction? of course downward because tension force counteract the pull of gravity.

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can you draw the arrow to represent the forces acting on the pen 100percent plss
:) of course
the tension force ⬆ , the gravity force⬇ ^_^