$A$ wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is $8 \ m/s$. The speed of the particle on the rim of the wheel at the same level as the centre of the wheel will be

$A$ wheel of radius $2 \ cm$ is at rest on a horizontal surface. $A$ point $P$ on the circumference of the wheel is in contact with the horizontal surface. When the wheel rolls without slipping on the surface,the displacement of point $P$ after half a rotation of the wheel is:

$A$ cylinder rolls without slipping down an inclined plane. The number of degrees of freedom it has is:

$A$ disc is performing pure rolling on a surface. The positions of $P$ and $Q$ at an instant are shown in the figure. $C$ is the center of the disc. Which of the following is true for their velocities at the instant when $P$ and $Q$ are at the same distance from the center?

$A$ solid sphere is moving on a horizontal plane. The ratio of its translational kinetic energy to its rotational kinetic energy is:

$A$ heavy solid sphere is thrown on a horizontal rough surface with initial velocity $u$ without rolling. What will be its speed when it starts pure rolling motion?