The total kinetic energy of a body of mass $10\ kg$ and radius $0.5\ m$ moving with a velocity of $2\ m/s$ without slipping is $32.8\ joule$.  The radius of gyration of the body is  .......... $m$

  • A

    $0.25$

  • B

    $0.2$

  • C

    $0.5$

  • D

    $  0.4$

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  • [AIIMS 2009]

Two discs of moments of inertia $I_1$ and $I_2$ about their respective axes (normal to  the disc and passing through the centre), and rotating with angular speed $\omega _1$ and $\omega _2$ are  brought into contact face to face with their axes of rotation coincident. What is the  loss in kinetic energy of the system in the process ?