An elastic collision takes place between two bodies $X$ and $Y$. The mass of body $X$ is $m$ and the mass of body $Y$ is $4m$. Before the collision, body $X$ moves with speed $v$, and after the collision it moves in the opposite direction with speed $\frac{3v}{5}$. Body $Y$ is at rest before the collision. What is the kinetic energy of body $Y$ after the collision?
- A$\frac{8}{10}mv^2$
- B$\frac{34}{50}mv^2$
- C$\frac{16}{50}mv^2$
- D$\frac{1}{5}mv^2$