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JCECE Engineering JCECE Engineering Solved Paper-2015

  • question_answer
    A sphere of mass \[m\] moving with a constant velocity \[u\] hits another stationary sphere of the same mass and of coefficient of restitution\[(e)\]. The ratio of velocities of the two spheres, after collision will be

    A) \[\frac{1-e}{1+e}\]                                         

    B) \[\frac{e}{e+1}\]

    C) \[2/e\]                                 

    D)  \[\frac{e+1}{2e}\]

    Correct Answer: A

    Solution :

    Given,\[{{m}_{1}}={{m}_{2}}=m,\,\,{{u}_{1}}=u\]and\[{{u}_{2}}=0\] Let \[{{v}_{1}}\] and \[{{v}_{2}}\] be their velocities after collision. According to momentum conservation,                 \[mu=m({{v}_{1}}+{{v}_{2}})\] or            \[u={{v}_{1}}+{{v}_{2}}\]                                              ... (i) By definition\[e=\frac{{{v}_{2}}-{{v}_{1}}}{u-0}\] or            \[{{v}_{2}}-{{v}_{1}}=eu\]                                            ... (ii) Solving Eqs. (i) and (ii), we have                 \[{{v}_{1}}=\frac{(1-e)u}{2}\] and        \[{{v}_{2}}=\left( \frac{1+e}{2} \right)u\] \[\Rightarrow \]               \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{1-e}{1+e}\]


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