$A$ round body is given a translational velocity and released on a surface that has friction. Then:

$A$ spool consists of a cylinder of radius $R_1$ wrapped with thread,and its end caps have radius $R_2$ as shown in the end view illustrated in the figure. The mass of the spool,including the thread,is $m$,and its moment of inertia about an axis through its center is $I$. The spool is placed on a rough horizontal surface so that it rolls without slipping. When a force $\vec{T}$ acting to the right is applied to the free end of the thread,the friction force exerted by the surface on the spool is given by:

$A$ 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)

$A$ solid sphere of mass $1 \ kg$ is rolling on a rough table with a linear speed of $1 \ m/s$. Its total kinetic energy is ....... $J$.

$A$ wheel of radius $1 \text{ m}$ rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is

$A$ thin uniform circular disc rolls with a constant velocity without slipping on a horizontal surface. Its total kinetic energy is