Two identical particles move towards each other with velocity $2v$ and $v$ respectively. The velocity of centre of mass is
(1) $v$
(2) $v/3$
(3) $v/2$
(4) zero

A body of mass 2 kg moving with a speed of $4\mathrm{~m~s}^{-1}$ makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed. The speed of the two body centre of mass is $\frac{x}{10}$ m/s. Find the value of $x$.

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) $4 : 1$

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) $4:3$