KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    A square of mass M and sides of length L has a moment of inertia Io when rotated about an axis perpendicular to its surface and passing through its center, as shown. Now a lump of clay, also of mass M is attached to one corner of the square as shown. What is the new moment of inertia of the masses about the same axis of rotation?

    A) \[{{I}_{0}}+\frac{M{{L}^{2}}}{4}\]

    B) \[{{I}_{0}}+\frac{M{{L}^{2}}}{2}\]

    C) \[{{I}_{0}}+\frac{\sqrt{2}M{{L}^{2}}}{2}\]   

    D) \[{{I}_{0}}+2M{{L}^{2}}\]

    Correct Answer: B

    Solution :

    The moment of inertia for the system can be calculated by adding the two individual moments of inertia as following
    \[{{I}_{clay}}=M{{\left( \sqrt{2}\frac{L}{2} \right)}^{2}}=\frac{M{{L}^{2}}}{2}\]

You need to login to perform this action.
You will be redirected in 3 sec spinner