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EAMCET Medical EAMCET Medical Solved Paper-1997

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

    A)  1.2 m/s                               

    B)  2\[\sqrt{2}\] m/s

    C)  20 m/s                                

    D)  2 m/s

    Correct Answer: B

    Solution :

                     Rotational kinetic energy of the thin metal \[disc\,{{E}_{K(rot)}}=\frac{1}{2}I{{\omega }^{2}}\]and \[I=\frac{m{{R}^{2}}}{2}\] \[{{E}_{K\left( rot \right)}}=\frac{1}{2}I\frac{{{v}^{2}}}{{{r}^{2}}}\] \[{{E}_{K(rot)}}=\frac{1}{4}m{{r}^{2}}\times \frac{{{v}^{2}}}{{{r}^{2}}}\] \[4=\frac{1}{4}m{{v}^{2}}\] \[{{v}^{2}}=\frac{4\times 4}{m}=\frac{4\times 4}{2}=8\] \[v=\sqrt{8}=2\sqrt{2}\,m/s\]


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