A body of mass $m$ slides down an incline and reaches the bottom with a velocity V . If the same mass were in the form of a disc which rolls down this incline, the velocity of the disc at bottom would have been
The radius of gyration of a circular disc of radius R and mass m rotating about diameter as axis is
A thin uniform metal rod of mass ' $M$ ' and length ' $L$ ' is swinging about a horizontal axis passing through its end. Its maximum angular velocity is ' $\omega$ '. Its centre of mass rises to a maximum height of ( $\mathrm{g}=$ Acceleration due to gravity)
Three thin rods, each of mass ' $M$ ' and length ' $L$ ' are placed along $\mathrm{X}, \mathrm{Y}$ and Z axes which are mutually perpendicular. One end of each rod is at origin. M. I. of the system about Z axis is