$A$ rigid body consists of a $3 \ kg$ mass and a $2 \ kg$ mass connected by a massless rod. The $3 \ kg$ mass is at $\vec{r}_1 = (2 \hat{i} + 5 \hat{j}) \ m$ and the $2 \ kg$ mass is at $\vec{r}_2 = (4 \hat{i} + 2 \hat{j}) \ m$. Find the length of the rod and the coordinates of the center of mass.

• A
  $\sqrt{17} \ m, \left( 4 \hat{i} + \frac{19}{5} \hat{j} \right) \ m$
• B
  $\sqrt{13} \ m, \left( \frac{14}{5} \hat{i} + \frac{19}{5} \hat{j} \right) \ m$
• C
  $\sqrt{11} \ m, \left( \frac{12}{5} \hat{i} + \frac{15}{4} \hat{j} \right) \ m$
• D
  $\sqrt{15} \ m, \left( \frac{14}{3} \hat{i} + \frac{13}{2} \hat{j} \right) \ m$