F=ma 2018 Part B Problem 23

Two particles with mass m_{1} and m_{2} are connected by a massless rigid rod of length L and placed on a horizontal frictionless table. At time t=0, the first mass receives an impulse perpendicular to the rod, giving it speed v. At this moment, the second mass is at rest. The next time the second mass is at rest is

Answer Choices
A. t=2 \pi L / v
B. t=\pi\left(m_{1}+m_{2}\right) L / m_{2} v
C. t=2 \pi m_{2} L /\left(m_{1}+m_{2}\right) v
D. t=2 \pi m_{1} m_{2} L /\left(m_{1}+m_{2}\right)^{2} v
E. t=2 \pi m_{1} L /\left(m_{1}+m_{2}\right) v