When two identical balls are moving with equal speeds in opposite directions, which of the following is true for the system of two bodies?

When two identical balls are moving with equal speeds in opposite directions, then momentum is zero, and kinetic energy is not zero. 

Let the mass of the balls be $m_1$ and $m_2$ and their velocities $v_1$ and $v_2$ respectively.

$m_1=m_2,v_1=-v_2$

Total momentum,
 

${\overrightarrow{p}}_{total}=m_1\overrightarrow{v_1}+m_2\overrightarrow{u_2}$

Two identical balls are moving at equal speeds in opposite directions

so

${\overrightarrow{p}}_{total}=m_1\overrightarrow{v_1}-m_1\overrightarrow{v_1}=0$

Total kinetic energy,

$E={\displaystyle \frac{1}{2}}{m}_1{v}_1^2+{\displaystyle \frac{1}{2}}{m}_2{v}_2^2$
 

$E=\frac{1}{2}{m}_1{v}_1^2+\frac{1}{2}{m}_1{v}_1^2= m_1{v}_1^2$