$A$ stationary body explodes into three pieces. The momenta of two pieces are $2p\,\hat{i}$ and $p\,\hat{j}$ respectively,where $p$ is a positive constant. The third piece will have:

• A
  a momentum of magnitude $3p$.
• B
  a momentum of magnitude $\sqrt{5}p$.
• C
  a momentum making an angle of $\tan^{-1}(1/4)$ with the $X$-axis.
• D
  a momentum making an angle of $\pi - \tan^{-1}(1/\sqrt{2})$ with the $X$-axis.