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NEET Sample Paper NEET Sample Test Paper-22

  • question_answer
    Two particles of masses\[{{m}_{1}}\]and\[{{m}_{2}}\]in projectile motion have velocities\[{{\vec{u}}_{1}}\]and \[{{\vec{u}}_{2}}\]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\[\left| ({{m}_{1}}{{{\vec{v}}}_{1}}+{{m}_{2}}{{{\vec{v}}}_{2}})-({{m}_{1}}{{{\vec{v}}}_{1}}+{{m}_{2}}{{{\vec{v}}}_{2}}) \right|\]

    A)  0                                

    B) \[({{m}_{1}}+{{m}_{2}})g{{t}_{0}}\]                

    C) \[2({{m}_{1}}+{{m}_{2}})g{{t}_{0}}\]              

    D) \[\frac{1}{2}({{m}_{1}}+{{m}_{2}})g{{t}_{0}}\] 

    Correct Answer: C

    Solution :

    \[\left| ({{m}_{1}}{{{\vec{v}}}_{1}}+{{m}_{2}}{{{\vec{v}}}_{2}})-({{m}_{1}}{{{\vec{u}}}_{1}}+{{m}_{2}}{{{\vec{u}}}_{2}}) \right|\] \[\text{=}\left| \text{change}\,\text{in momentum of the two particle} \right|\] \[\text{=}\left| \text{external}\,\text{force}\,\text{on}\,\text{ethe}\,\text{system}\,\text{X}\,\text{time}\,\text{interval} \right|\] \[=({{m}_{1}}{{m}_{2}})g(2{{t}_{0}})\] \[=2({{m}_{1}}+{{m}_{2}})g{{t}_{0}}\] Hence, the correction option is [c].


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