Answer
The mass of the system increases by $1.0\times 10^{-14}~kg$
Work Step by Step
We can assume that the kinetic energy that is lost is converted into additional mass. We can find the initial kinetic energy:
$K = \frac{1}{2}m_1~v^2 + \frac{1}{2}m_2~v^2$
$K = \frac{1}{2}(1.00~kg)(30.0~m/s)^2 + \frac{1}{2}(1.00~kg)~(30.0~m/s)^2$
$K = 900~J$
We can find the increase in mass:
$E = 900~J$
$mc^2 = 900~J$
$m = \frac{900~J}{c^2}$
$m = \frac{900~J}{(3.0\times 10^8~m/s)^2}$
$m = 1.0\times 10^{-14}~kg$
The mass of the system increases by $1.0\times 10^{-14}~kg$.
