Two particles of masses \[{{m}_{1}}\] and \[{{m}_{2}}\] in projectile motion have velocities \[{{\vec{v}}_{1}}\] and \[{{\vec{v}}_{2}}\] respectively at time t = 0. They collide at time \[{{t}_{0}}\]. Their velocities become \[{{\vec{v}}_{1}}'\] and \[{{\vec{v}}_{2}}'\] at time \[2{{t}_{0}}\] while still moving in air. The value of \[|({{m}_{1}}\overrightarrow{{{v}_{1}}}'\,+{{m}_{2}}\overrightarrow{{{v}_{2}}}')-({{m}_{1}}\overrightarrow{{{v}_{1}}}\,+{{m}_{2}}\overrightarrow{{{v}_{2}}})\]| is [IIT-JEE Screening 2001]

• A.             Zero    
• B.             \[({{m}_{1}}+{{m}_{2}})g{{t}_{0}}\]
• C.             \[2({{m}_{1}}+{{m}_{2}})g{{t}_{0}}\]
• D.               \[\frac{1}{2}({{m}_{1}}+{{m}_{2}})g{{t}_{0}}\]