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NEET Physics Rotational Motion NEET PYQ-Rotational Motion

  • question_answer
    Three objects, A : (a solid sphere), B : (a thin circular disk) and C : (a circular ring), each have the same mass M and radius R. They all spin with the same angular speed \[\omega \] about their own symmetry axes. The amounts of work (W) required to bring them to rest, would satisfy the relation                                              [NEET - 2018]

    A) \[{{\text{W}}_{\text{B}}}\text{}{{\text{W}}_{\text{A}}}\text{}{{\text{W}}_{\text{C}}}\]

    B) \[{{\text{W}}_{\text{A}}}\text{}{{\text{W}}_{\text{B}}}\text{}{{\text{W}}_{\text{C}}}\]

    C) \[{{\text{W}}_{\text{C}}}\text{}{{\text{W}}_{\text{B}}}\text{}{{\text{W}}_{\text{A}}}\]

    D) \[{{\text{W}}_{\text{A}}}\text{}{{\text{W}}_{\text{C}}}\text{}{{\text{W}}_{\text{B}}}\]

    Correct Answer: C

    Solution :

    [c] Work done required to bring them rest
    \[\Delta \text{W=}\Delta \text{KE}\]
    \[\Delta W=\frac{1}{2}|{{\omega }^{2}}\]
    \[\Delta W\propto \text{l}\] for same \[\omega \]
    \[{{\text{W}}_{\text{A}}}\text{:}{{\text{W}}_{\text{B}}}\text{:}{{\text{W}}_{\text{C}}}\text{=}\frac{\text{2}}{\text{5}}\text{M}{{\text{R}}^{\text{2}}}\text{:}\frac{\text{1}}{\text{2}}\text{M}{{\text{R}}^{\text{2}}}\text{:M}{{\text{R}}^{\text{2}}}\]
    \[\text{=}\frac{2}{5}:\frac{1}{2}:1\]
    \[=4:5:10\]
    \[\Rightarrow {{\text{W}}_{\text{C}}}\text{}{{\text{W}}_{\text{B}}}\text{}{{\text{W}}_{\text{A}}}\]


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