two people- one twice as heavy as the other one, play tug-of-war with a 12m ideal rope while standing on a frctionless ice surface.Would any of them move and if he does, how far?explain why.

Answer 1

Their center of gravity would not move because there is no net force on the system comprising the two masses.
Say they start a distance d apart
the 2m mass is at x = 0
the 1 m mass is at x = d
Then the center of gravity is at
2m Xcg = m (d-Xcg)
2 Xcg = d - Xcg
Xcg = d/3
which is where it stays.