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KVPY Sample Paper KVPY Stream-SX Model Paper-14

  • question_answer
    Two masses \[{{m}_{1}}\]and \[{{m}_{2}}({{m}_{1}}>{{m}_{2}})\]are connected by a light spring. This system is placed on a horizontal frictionless table. At \[t=0,\]blocks are pushed closer by compressing the spring and then released. The system oscillates with a time period T. Time period of oscillation of centre of mass of system is  

    A) \[\frac{{{m}_{1}}+{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}\cdot T\]

    B) \[\frac{{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}}\cdot T\]

    C) \[\frac{{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}\cdot T\]   

    D) zero

    Correct Answer: D

    Solution :

    As system is released at \[t=0,\]momentum of system at any instant  t is \[p(t)={{M}_{\text{system}}}\times {{v}_{CM}}={{p}_{\text{system}}}(t=0)=0\] \[\therefore \]\[{{v}_{CM}}=0\] So, centre of mass of system is always at rest and is not oscillating.


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