Since , no external force is present on the system . So conservation principle of momentum is applicable .

`:.`           `vec(p_i) = vec(p_f) = vec (p_1) + vec(p_2)`

`:.`          ` vec (p_1) = - vec (p_2)`                                               (  `because    vec (p_i) = 0)`

`:.`         l`vec(p_1)`l =  l - `vec(p_2)`l

`:.`       `vec(p_1) = vec(p_2)`

From this point of view, it is clear that moments of both  particles are equal in magnitude but opposite in direction .

Also friction is absent . So total mechanical energy of system remains conserved .