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Chhattisgarh PMT Chhattisgarh PMT Solved Paper-2004

  • question_answer
    A particle is making uniform circular motion with angular momentum J. If its kinetic energy is made half and angular frequency be doubled, its new angular momentum will be

    A)  2J                                          

    B)  4J

    C)  J/2                                        

    D)  J/4

    Correct Answer: D

    Solution :

    Angular momentum  \[J=I\omega \]       ??(i) and rotational kinetic energy \[KE=\frac{1}{2}I{{\omega }^{2}}\]?.(ii) From these two, we get                                \[J=\frac{2KE}{\omega }\]   So, according to the question                 \[\frac{{{J}_{2}}}{{{J}_{1}}}=\frac{K{{E}_{2}}}{K{{E}_{1}}}\times \frac{{{\omega }_{1}}}{{{\omega }_{2}}}\] or            \[\frac{{{J}_{2}}}{J}=\frac{1}{2}\times \frac{1}{2}\] \[\Rightarrow \]               \[{{J}_{2}}=J/4\]


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