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NEET Sample Paper NEET Sample Test Paper-83

  • question_answer
    The moment of inertia of a thin square plate ABCD (figure) of uniform thickness about an axis passing through the centre of and perpendicular to the plane of plate is

    A)  \[{{l}_{1}}+{{l}_{3}}\]                      

    B)  \[{{l}_{2}}+{{l}_{3}}+{{l}_{4}}\]    

    C)  \[{{l}_{2}}+{{l}_{3}}\]                      

    D)  \[{{l}_{1}}+{{l}_{2}}+{{l}_{3}}+{{l}_{4}}\]

    Correct Answer: A

    Solution :

    Applying the theorem of perpendicular axes \[{{l}_{0}}={{l}_{1}}+{{l}_{2}}={{l}_{3}}+{{l}_{4}}\] From symmetry of axes\[{{l}_{1}}\,\,and\,\,{{l}_{2}}\] and \[{{l}_{3}}\,\,and\,\,{{l}_{4}}\] \[\therefore \,\,\,\,\,\,\,\,\,{{l}_{0}}=2{{l}_{2}}=2{{l}_{3}}\,\,i.e.,\,\,{{l}_{2}}={{l}_{3}}\] Now,      \[{{l}_{0}}={{l}_{1}}+{{l}_{3}}\]


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