Question

A particle of mass 2m is connected by an inextensible string of length 1.2m to a ring of mass m

Answer 1

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Answer 2

Answer: x = 0.8m

Solution:  

Let us assume, there is no outer force acting on the system in horizontal direction. Also given friction is negligible and the gravitational force is acting vertically on the system. The tension force of the system is inner force. In this situation, the center mass of the system can't move in horizontal direction. In general, the center can be found as,

Mass m  = 2m

Length l = 1.2m  

Let x = distance from the center from the initial position of the ring

                $mx = (l - x) \times (mass)\\mx = (1.2 - x) \times 2m\\mx = 2.4m - 2mx\\3mx = 2.4m\\x = 2.4/3\\x = 0.8$

when the string is vertical, both masses and the center of mass of the system are on the same vertical line  

therefore the ring had travelled x = 0.8m