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CMC Medical CMC-Medical VELLORE Solved Paper-2015

  • question_answer
    A ball of mass m moving with velocity v strikes the bob of a pendulum at rest. The mass of the bob is also m. If the collision is perfectly inelastic, the height upto which the bob will go up, is given by

    A)  \[\frac{{{v}^{2}}}{3\,g}\]                                             

    B)  \[\frac{{{v}^{2}}}{4\,g}\]

    C)  \[\frac{{{v}^{2}}}{3\,g}\]                                             

    D)  \[\frac{{{v}^{2}}}{6\,g}\]

    E)  \[\frac{{{v}^{2}}}{8\,g}\]

    Correct Answer: E

    Solution :

                    The collision is perfectly inelastic, hence the two balls sticks together. From conservation of energy, \[2mV=mv\] \[\Rightarrow \]                     \[V=\frac{v}{2}\] Now, from the principal of conservation of energy \[2mgh=\frac{1}{2}(2m)\,{{V}^{2}}\]           \[=\frac{1}{2}(2m)\,{{\left( \frac{v}{2} \right)}^{2}}\] \[\Rightarrow \]                     \[h=\frac{{{v}^{2}}}{8g}\]


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