A solid sphere is rolling without slipping on a horizontal surface. The ratio of its rotational kinetic energy to its translational kinetic energy is

A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, $A$ is the point of contact, $B$ is the centre of the sphere and $C$ is its topmost point. Then,

A solid sphere, a hollow sphere and a disc, all having same mass and radius are placed at the top of an incline and released. The friction coefficients between the objects and the incline are the same and not sufficient to allow pure rolling. The smallest kinetic energy at the bottom of the incline will be achieved by:

A solid sphere, a hollow sphere and a disc all having the same mass and radius, are placed at the top of an incline and released. The friction coefficients between the objects and the incline are same and not sufficient to allow pure rolling. The least time will be taken in reaching the bottom by:

A large spool of rope lies on the ground as shown in the fig: The end, labelled $X$ is pulled a distance $S$ in the horizontal direction. The spool rolls without slipping The centre of mass of the spool moves a. distance

A thin string is wrapped several times around a cylinder kept on a rough horizontal surface. A boy standing at a distance $\ell$ from the cylinder draws the string towards him as shown in figure. The cylinder rolls without slipping. The length of the string passed through the hand of the boy while the cylinder reaches his hand is