Answer
(a) No, there is no net external force acting on the system.
(b) $m_B/m_A$
(c) $m_B/m_A$
(d) The center of mass remains at rest.
Work Step by Step
(a) No, there is no net external force acting on the system.
(b) We can use conservation of momentum to set up an equation.
$m_A~v_A = m_B~v_B$
$v_A/v_B = m_B/m_A$
(c) $\frac{KE_A}{KE_B} = \frac{\frac{1}{2}m_Av_A^2}{\frac{1}{2}m_Bv_B^2} = (\frac{v_A}{v_B})^2\times (\frac{m_A}{m_B}) = (\frac{m_B}{m_A})^2\times (\frac{m_A}{m_B}) = \frac{m_B}{m_A}$
(d) Since the center of mass was at rest initially, by conservation of momentum, the center of mass will remain at rest because there is no net external force acting on the system.