Velocity of Centre of Mass

Questions asking to find the velocity (or speed) of the centre of mass of a system of particles, without involving an actual collision outcome.

jee-main 2022 Q4 View

A body of mass 8 kg and another of mass 2 kg are moving with equal kinetic energy. The ratio of their respective momenta will be
(1) $1 : 1$
(2) $2 : 1$
(3) $1 : 4$
(4) $4 : 1$

jee-main 2023 Q5 View

Two bodies are having kinetic energies in the ratio $16:9$. If they have same linear momentum, the ratio of their masses respectively is:
(1) $3:4$
(2) $9:16$
(3) $16:9$
(4) $4:3$