When two bodies of masses\[{{m}_{1}}\]and\[{{m}_{2}}\]moving with velocities\[{{u}_{1}}\]and\[{{u}_{2}}\]in the opposite direction collide with each other and move together after collision in the same direction with a common velocity v, then

• A.  \[{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}v+{{m}_{2}}v\]
• B.  \[{{m}_{2}}{{u}_{1}}-{{m}_{1}}{{u}_{2}}=({{m}_{1}}+{{m}_{2}})v\]
• C.  \[{{m}_{1}}{{u}_{1}}-{{m}_{2}}{{u}_{2}}=({{m}_{1}}-{{m}_{2}})v\]
• D.  \[v=\frac{{{m}_{1}}{{u}_{1}}-{{m}_{2}}{{u}_{2}}}{{{m}_{1}}+{{m}_{2}}}\]