i assume that a minimum force, F is required to initiate an acceleration clockwise by finding the force for balance.

By gear ratio,

F*(100) = F'(200) where F' is the equivalent force on the big gear on the right!

by principle of moment on the right gear,

total moment = 0

F'*200 = 1kN*(500)    ( i assume the kilo refers to kilo newton)
F(1/2)*200 =  1kN*(500)
F = 5 kN
therefore, minimum force required to set the system in motion is F > 5kN

Am i correct ?

the 180 degrees appears to be a trick question as once the system can move, the angular displacement will be achieved after some time.

you can model your simulation using EJS to engage in deep learning and you will learn a lot of stuff besides the answers to this question.

I welcome you to challenge yourself and immersed in a truly deep ICT tool for learning.  ;D