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J & K CET Medical J & K - CET Medical Solved Paper-2007

  • question_answer
    A thin metal disc of radius of 0.25 m and mass 2 kg starts from rest and rolls down on an inclined plane. If its rotational kinetic energy is 4 J at the foot of inclined plane, then the linear velocity at the same point, is in m/s

    A)  2                                            

    B)  \[2\sqrt{2}\]

    C)  \[2\sqrt{3}\]                                     

    D)  \[3\sqrt{2}\]

    Correct Answer: B

    Solution :

                     Rotational kinetic energy \[=\frac{1}{2}I{{\omega }^{2}}\] \[\therefore \]Rotational \[KE=\frac{1}{2}\left[ \frac{1}{2}m{{r}^{2}} \right]\frac{{{v}^{2}}}{{{r}^{2}}}\]                 \[\left( where\,I=\frac{1}{2}m{{r}^{2}} \right)\]                 \[4=\frac{1}{2}\left[ \frac{1}{2}(2){{r}^{2}} \right]=\frac{{{v}^{2}}}{{{r}^{2}}}\] \[\Rightarrow \]               \[{{v}^{2}}=8\]                 \[v=2\sqrt{2}m/s\]


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