A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $\frac{x}{5}$. The value of $x$ is________.

A solid sphere rolls without slipping, first horizontally and then up to a point $X$ at height $h$ on an inclined plane before rolling down, as shown in the figure below. The initial horizontal speed of the sphere is

A circular disc is rolling on a horizontal plane. Its total kinetic energy is  $300\,\,J.$  ......... $J$ is its translational  $K.E.$

A thin uniform rod oflength $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end . Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of:

If a solid sphere of mass $1\, kg$ and radius $0.1\, m$ rolls without slipping at a uniform velocity of $1\, m/s$ along a straight line on a horizontal floor, the kinetic energy is

A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity $\omega$. A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If $E$ be the initial Kinetic energy of the system, then final Kinetic energy will be $\frac{E}{x}$.The value of $x$ is $....$