$A$ bomb of mass $m$ is projected from the ground with speed $v$ at an angle $\theta$ with the horizontal. At the maximum height from the ground,it explodes into two fragments of equal mass. If one fragment comes to rest immediately after the explosion,then the horizontal range of the centre of mass is ..............

• A
  $\frac{v^2 \sin^2 \theta}{g}$
• B
  $\frac{v^2 \sin \theta}{g}$
• C
  $\frac{v^2 \sin \theta}{2g}$
• D
  $\frac{v^2 \sin 2\theta}{g}$