The problem is solved using conservation of energy. The initial energy is:
$\begin{align*}2 \sqrt{m^2 c^4 + p^2 c^4}\end{align*}$
The initial momentum $p$ can be found from the definition of relativistic momentum
$\begin{align*}p := \frac{m u}{\sqrt{1 - u^2/c^2}} = \frac{m(3/5)c }{\sqrt{1 - 9/25}} = (3/5) mc / (4/5) = (3/4) mc\end{align*...$
Thus, the initial energy is
$\begin{align*}2 \sqrt{m^2 c^4 + p^2 c^4} = 2 \sqrt{m^2 c^4 + ((3/4) m c)^2 c^2} = 2 m c^2 \sqrt{1 + 9/16} = 2 m c^2 (5/4) = (...$
Because there is only mass after the collision, and the total initial momentum is 0, the mass after the collision must be at rest. Therefore its energy is $m' c^2$ . Equating this with the initial total energy, we find that
$\begin{align*}m' c^2 = (5/2) mc^2 \Rightarrow m' = (5/2) m = 5/2 \cdot 4 \mbox{ kg} = \boxed{ 10 \mbox{ kg}}\end{align*}$
Therefore, answer (D) is the correct answer.

Solution to 1996 Problem 36