$A$ uniform sphere of mass $500 \; g$ rolls without slipping on a plane horizontal surface with its centre moving at a speed of $5.00 \; cm/s$. Its kinetic energy is

$A$ solid sphere is in rolling motion. In rolling motion,a body possesses translational kinetic energy $(K_t)$ as well as rotational kinetic energy $(K_r)$ simultaneously. The ratio $K_t : (K_t + K_r)$ for the sphere is

An object is rolling on a horizontal surface without slipping. If its rotational kinetic energy and translational kinetic energy are equal,the object is a:

$A$ disc is rolling without slipping on a surface. The radius of the disc is $R$. At $t=0$,the top most point on the disc is $A$ as shown in the figure. When the disc completes half of its rotation,the displacement of point $A$ from its initial position is

$A$ string is wound around a hollow cylinder of mass $5\, kg$ and radius $0.5\, m$. If the string is now pulled with a horizontal force of $40\, N$,and the cylinder is rolling without slipping on a horizontal surface (see figure),then the angular acceleration of the cylinder will be ......... $rad/s^2$. (Neglect the mass and thickness of the string)

$A$ uniform non-deformable cylinder of mass $m$ and radius $R$ is rolling without slipping on a horizontal rough surface. The force of friction is