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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2012

  • question_answer
    A ball of mass m moving with a velocity\[\mu \]collides head-on with another ball of mass m initially at rest. If the coefficient of restitution be e, then the ratio of the final and initial velocities of the first ball is

    A)  \[\frac{1-e}{2}\]

    B)  \[\frac{1+e}{2}\]

    C)  \[\frac{1-e}{1+e}\]

    D)  \[\frac{1+e}{1-e}\]

    Correct Answer: D

    Solution :

     Given, \[{{m}_{1}}={{m}_{2}}=m,{{u}_{1}}=u\] and      \[{{u}_{2}}=0\] \[\therefore \] \[{{v}_{1}}={{u}_{1}}=\frac{({{m}_{1}}-e{{m}_{2}})}{({{m}_{1}}+{{m}_{2}})}+{{u}_{2}}\frac{(1+e){{m}_{2}}}{({{m}_{1}}+{{m}_{2}})}\] \[=\frac{u(1-e)}{2}\] \[\Rightarrow \] \[\frac{{{v}_{1}}}{u}=\left( \frac{1-e}{2} \right)\]


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