RAJASTHAN PMT Rajasthan - PMT Solved Paper-2008

  • question_answer
    A particle performing uniform circular motion has angular momentum L. If its angular frequency is doubled and its kinetic energy is halved, then the new angular momentum is

    A)  \[\frac{L}{4}\]                                  

    B)  \[2L\]

    C)  \[4L\]                  

    D)         \[\frac{L}{2}\]

    Correct Answer: A

    Solution :

    Angular momentum                 \[L=I\omega \]                                                  ... (i) Kinetic energy,                 \[K=\frac{1}{2}I{{\omega }^{2}}=\frac{1}{2}L\omega \]  {from Eq. (i)} \[\therefore \]  \[L=\frac{2K}{\omega }\] Now      \[L=\frac{2\left( \frac{K}{2} \right)}{2\omega }\] \[\Rightarrow \]               \[L=\frac{L}{4}\]


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