A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 m/s. Which of the following statements are correct for the system of these two masses?

The following figure depicts the situation.

$$\begin{gathered} \mathrm{u} = -2 + 5\mathrm{v} ----\left(1\right) \\ \mathrm{u} = 2 + \mathrm{v} ----\left(1\right) \end{gathered}$$

Solving, we get

$\mathrm{u} = 3{\mathrm{ms}}^{-1}$

The momentum of the system is 1x 3 = 3 kg m/s;
momentum of 5 kg after collision is 5x1= 5 kg m/s.
Thus, the kinetic energy of the centre of mass is

$\frac{1}{2}\left({\mathrm{m}}_1 + {\mathrm{m}}_2\right){\left(\frac{{\mathrm{m}}_1\mathrm{u}}{{\mathrm{m}}_1 + {\mathrm{m}}_2}\right)}^2 = \frac{1}{2}\left(1 + 5\right){\left(\frac{1 \mathrm{x} 3}{6}\right)}^2 = 0.75 \mathrm{J}$The total kinetic energy of the system is calculated as

$\frac{1}{2} \mathrm{x} 1 \mathrm{x} 3^2 = 4.5 \mathrm{J}$