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 .......... $m$
$0.25$
$0.2$
$0.5$
$ 0.4$
A body of moment of inertia of $3\ kg-m^2$ rotating with an angular velocity of $2\ rad/sec$ has the same kinetic energy as a mass of $12\ kg$ moving with a velocity of .......... $m/s$
$A$ sphere of mass $M$ and radius $R$ is attached by a light rod of length $l$ to $a$ point $P$. The sphere rolls without slipping on a circular track as shown. It is released from the horizontal position. the angular momentum of the system about $P$ when the rod becomes vertical is :
An air compressor is powered by a $200\,rad\,s^{-1}$ electric motor using a $V-$ belt drive. The motor pulley is $8\,cm$ in radius, and the tension in the $V-$ belt is $135\,N$ on one side and $45\,N$ on the other. The power of the motor will be ...... $kW$.
A disc is rolling without slipping on a straight surface. The ratio of its translational kinetic energy to its total kinetic energy is
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 ?