A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass $K$. If radius of the ball be $R$, then the fraction of total energy associated with its rotational energy will be
$\frac{{{K^2}}}{{{R^2}}}$
$\frac{{{K^2}}}{{{K^2} + {R^2}}}$
$\frac{{{R^2}}}{{{K^2} + {R^2}}}$
$\frac{{{K^2} + {R^2}}}{{{R^2}}}$
An energy of $484\,J$ is spent in increasing the speed of a flywheel from $60\,rpm$ to $360\,rpm$. The moment of inertia of the flywheel is $.............\,kg - m ^2$
A hollow sphere of mass $m$ filled with a non-viscous liquid of same mass $m$ is released on a slope inclined at angle $q$ with the horizontal. The friction between the sphere and the slope is sufficient to prevent sliding and frictional forces between the inner surface of the sphere and the liquid is negligible. After descending a certain height ratio of translational and rotational kinetic energies is found to be $x:y$, find the numerical value of expression $(x+y)_{min}.$
A circular disc is rolling on a horizontal plane. Its total kinetic energy is $300\,\,J.$ ......... $J$ is its translational $K.E.$
A wheel is rotating with an angular speed of $20\,rad/sec$. It is stopped to rest by applying a constant torque in $4\ s$. If the moment of inertia of the wheel about its axis is $0.20\ kg-m^2$, then the work done by the torque in two seconds will be .......... $J$
A ring, a solid sphere and a thin disc of different masses rotate with the same kinetic energy. Equal torques are applied to stop them. Which will make the least number of rotations before coming to rest