Question

Consider a system of two identical particles having
mass m. If one of the particles of mass m is pushed
towards the center of mass of the particles through a
distance x, by what amount the other particle should
move so as to keep the center of mass of particles at
the original position?​

Answer 1

Answer:

Well the other particles must also move by a distance x towards the other mass so that everything remains symmetrical and the centre of mass of this system remains at the same place.

This can be clearly inferred from the equation that

∆Centre of mass = m1∆x1 + m2∆x2 / m 1+m2

and centre of mass shouldn't change

So,

m1∆x1 = -m2∆x2

and here,

m1=m2

So,

∆x1 = -∆x2

Negative sign showing that other particle should move in opposite direction to the one travelled by the first mass.

Hope this helps you !